Precalculus: Graphical, Numerical, Algebraic 8th Edition solutions

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercise numbers with a gray background indicate problems that the authors have designed to be solved without a calculator. In Exercises 14, rewrite the expression as a polynomial in standard form. 1. \(\frac{x^{3}-4 x^{2}+7 x}{x}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercise numbers with a gray background indicate problems that the authors have designed to be solved without a calculator. In Exercises 14, rewrite the expression as a polynomial in standard form. 2. \(\frac{2 x^{3}-5 x^{2}-6 x}{2 x}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercise numbers with a gray background indicate problems that the authors have designed to be solved without a calculator. In Exercises 14, rewrite the expression as a polynomial in standard form. 3. \(\frac{x^{4}-3 x^{2}+7 x^{5}}{x^{2}}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercise numbers with a gray background indicate problems that the authors have designed to be solved without a calculator. In Exercises 14, rewrite the expression as a polynomial in standard form. 4. \(\frac{6 x^{4}-2 x^{3}+7 x^{2}}{3 x^{2}}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercise numbers with a gray background indicate problems that the authors have designed to be solved without a calculator. In Exercises 510, factor the polynomial into linear factors. 5. \(x^{3}-4 x\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercise numbers with a gray background indicate problems that the authors have designed to be solved without a calculator. In Exercises 510, factor the polynomial into linear factors. 6. \(6 x^{2}-54\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercise numbers with a gray background indicate problems that the authors have designed to be solved without a calculator. In Exercises 510, factor the polynomial into linear factors. 7. \(4 x^{2}+8 x-60\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercise numbers with a gray background indicate problems that the authors have designed to be solved without a calculator. In Exercises 510, factor the polynomial into linear factors. 8. \(15 x^{3}-22 x^{2}+8 x\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercise numbers with a gray background indicate problems that the authors have designed to be solved without a calculator. In Exercises 510, factor the polynomial into linear factors. 9. \(x^{3}+2 x^{2}-x-2\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercise numbers with a gray background indicate problems that the authors have designed to be solved without a calculator. In Exercises 510, factor the polynomial into linear factors. 10. \(x^{4}+x^{3}-9 x^{2}-9 x\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 16, divide \(f(x)\) by \(d(x)\), and write a summary statement in polynomial form and fraction form. \(f(x)=x^{2}-2 x+3 ; d(x)=x-1\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 16, divide \(f(x)\) by \(d(x)\), and write a summary statement in polynomial form and fraction form. \(f(x)=x^{3}-1 ; d(x)=x+1\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 16, divide \(f(x)\) by \(d(x)\), and write a summary statement in polynomial form and fraction form. \(f(x)=x^{3}+4 x^{2}+7 x-9 ; d(x)=x+3\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 16, divide \(f(x)\) by \(d(x)\), and write a summary statement in polynomial form and fraction form. \(f(x)=4 x^{3}-8 x^{2}+2 x-1 ; d(x)=2 x+1\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 16, divide \(f(x)\) by \(d(x)\), and write a summary statement in polynomial form and fraction form. \(f(x)=x^{4}-2 x^{3}+3 x^{2}-4 x+6 ; d(x)=x^{2}+2 x-1\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 16, divide \(f(x)\) by \(d(x)\), and write a summary statement in polynomial form and fraction form. \(f(x)=x^{4}-3 x^{3}+6 x^{2}-3 x+5 ; d(x)=x^{2}+1\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 712, divide using synthetic division, and write a summary statement in fraction form. \(\frac{x^{3}-5 x^{2}+3 x-2}{x+1}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 712, divide using synthetic division, and write a summary statement in fraction form. \(\frac{2 x^{4}-5 x^{3}+7 x^{2}-3 x+1}{x-3}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 712, divide using synthetic division, and write a summary statement in fraction form. \(\frac{9 x^{3}+7 x^{2}-3 x}{x-10}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 712, divide using synthetic division, and write a summary statement in fraction form. \(\frac{3 x^{4}+x^{3}-4 x^{2}+9 x-3}{x+5}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 712, divide using synthetic division, and write a summary statement in fraction form. \(\frac{5 x^{4}-3 x+1}{4-x}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 712, divide using synthetic division, and write a summary statement in fraction form. \(\frac{x^{8}-1}{x+2}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1318, use the Remainder Theorem to find the remainder when (x) is divided by \(x-k\) . \(f(x)=2 x^{2}-3 x+1 ; k=2\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1318, use the Remainder Theorem to find the remainder when (x) is divided by \(x-k\) . \(f(x)=x^{4}-5 ; k=1\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1318, use the Remainder Theorem to find the remainder when (x) is divided by \(x-k\) . \(f(x)=x^{3}-x^{2}+2 x-1 ; k=-3\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1318, use the Remainder Theorem to find the remainder when (x) is divided by \(x-k\) . \(f(x)=x^{3}-3 x+4 ; k=-2\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1318, use the Remainder Theorem to find the remainder when (x) is divided by \(x-k\) . \(f(x)=2 x^{3}-3 x^{2}+4 x-7 ; k=2\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1318, use the Remainder Theorem to find the remainder when (x) is divided by \(x-k\) . \(f(x)=x^{5}-2 x^{4}+3 x^{2}-20 x+3 ; k=-1\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1924, use the Factor Theorem to determine whether the first polynomial is a factor of the second polynomial. \(x-1 ; x^{3}-x^{2}+x-1\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1924, use the Factor Theorem to determine whether the first polynomial is a factor of the second polynomial. \(x-3 ; x^{3}-x^{2}-x-15\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1924, use the Factor Theorem to determine whether the first polynomial is a factor of the second polynomial. \(x-2 ; x^{3}+3 x-4\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1924, use the Factor Theorem to determine whether the first polynomial is a factor of the second polynomial. \(x-2 ; x^{3}-3 x-2\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1924, use the Factor Theorem to determine whether the first polynomial is a factor of the second polynomial. \(x+2 ; 4 x^{3}+9 x^{2}-3 x-10\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1924, use the Factor Theorem to determine whether the first polynomial is a factor of the second polynomial. \(x+1 ; 2 x^{10}-x^{9}+x^{8}+x^{7}+2 x^{6}-3\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 25 and 26, use the graph to guess possible linear factors of \(f(x)\). Then completely factor \(f(x)\) with the aid of synthetic division. \(f(x)=5 x^{3}-7 x^{2}-49 x+51\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 25 and 26, use the graph to guess possible linear factors of \(f(x)\). Then completely factor \(f(x)\) with the aid of synthetic division. \(f(x)=5 x^{3}-12 x^{2}-23 x+42\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2730, find the polynomial function with leading coefficient 2 that has the given degree and zeros. Degree 3, with -2 , 1, and 4 as zeros

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2730, find the polynomial function with leading coefficient 2 that has the given degree and zeros. Degree 3, with -1, 3, and -5 as zeros

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2730, find the polynomial function with leading coefficient 2 that has the given degree and zeros. Degree 3, with 2, \(\frac{1}{2}\), and \(\frac{3}{2}\) as zeros

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2730, find the polynomial function with leading coefficient 2 that has the given degree and zeros. Degree 4, with -3, -1, 0, and \(\frac{5}{2}\) as zeros

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 31 and 32, using only algebraic methods, find the cubic function with the given table of values. Check with a grapher. \(\begin{array}{c|cccc} x & -4 & 0 & 3 & 5 \\ \hline f(x) & 0 & 180 & 0 & 0 \end{array}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 31 and 32, using only algebraic methods, find the cubic function with the given table of values. Check with a grapher. \(\begin{array}{c|cccc} x & -2 & -1 & 1 & 5 \\ \hline f(x) & 0 & 24 & 0 & 0 \end{array}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3336, use the Rational Zeros Theorem to write a list of all potential rational zeros. Then determine which ones, if any, are zeros. \(f(x)=6 x^{3}-5 x-1\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3336, use the Rational Zeros Theorem to write a list of all potential rational zeros. Then determine which ones, if any, are zeros. \(f(x)=3 x^{3}-7 x^{2}+6 x-14\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3336, use the Rational Zeros Theorem to write a list of all potential rational zeros. Then determine which ones, if any, are zeros. \(f(x)=2 x^{3}-x^{2}-9 x+9\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3336, use the Rational Zeros Theorem to write a list of all potential rational zeros. Then determine which ones, if any, are zeros. \(f(x)=6 x^{4}-x^{3}-6 x^{2}-x-12\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3740, use synthetic division to prove that the number k is an upper bound for the real zeros of the function . \(k=3 ; f(x)=2 x^{3}-4 x^{2}+x-2\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3740, use synthetic division to prove that the number k is an upper bound for the real zeros of the function . \(k=5 ; f(x)=2 x^{3}-5 x^{2}-5 x-1\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3740, use synthetic division to prove that the number k is an upper bound for the real zeros of the function . \(k=2 ; f(x)=x^{4}-x^{3}+x^{2}+x-12\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3740, use synthetic division to prove that the number k is an upper bound for the real zeros of the function . \(k=3 ; f(x)=4 x^{4}-6 x^{3}-7 x^{2}+9 x+2\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4144, use synthetic division to prove that the number k is a lower bound for the real zeros of the function . \(k=-1 ; f(x)=3 x^{3}-4 x^{2}+x+3\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4144, use synthetic division to prove that the number k is a lower bound for the real zeros of the function . \(k=-3 ; f(x)=x^{3}+2 x^{2}+2 x+5\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4144, use synthetic division to prove that the number k is a lower bound for the real zeros of the function . \(k=0 ; f(x)=x^{3}-4 x^{2}+7 x-2\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4144, use synthetic division to prove that the number k is a lower bound for the real zeros of the function . \(k=-4 ; f(x)=3 x^{3}-x^{2}-5 x-3\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4548, use the upper and lower bound tests to decide whether there could be real zeros for the function outside the window shown. If so, check for additional zeros. \(f(x)=6 x^{4}-11 x^{3}-7 x^{2}+8 x-34\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4548, use the upper and lower bound tests to decide whether there could be real zeros for the function outside the window shown. If so, check for additional zeros. \(f(x)=x^{5}-x^{4}+21 x^{2}+19 x-3\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4548, use the upper and lower bound tests to decide whether there could be real zeros for the function outside the window shown. If so, check for additional zeros. \(f(x)=x^{5}-4 x^{4}-129 x^{3}+396 x^{2}-8 x+3\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4548, use the upper and lower bound tests to decide whether there could be real zeros for the function outside the window shown. If so, check for additional zeros. \(f(x)=2 x^{5}-5 x^{4}-141 x^{3}+216 x^{2}-91 x+25\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4956, find all of the real zeros of the function, finding exact values whenever possible. Identify each zero as rational or irrational. \(f(x)=2 x^{3}-3 x^{2}-4 x+6\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4956, find all of the real zeros of the function, finding exact values whenever possible. Identify each zero as rational or irrational. \(f(x)=x^{3}+3 x^{2}-3 x-9\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4956, find all of the real zeros of the function, finding exact values whenever possible. Identify each zero as rational or irrational. \(f(x)=x^{3}+x^{2}-8 x-6\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4956, find all of the real zeros of the function, finding exact values whenever possible. Identify each zero as rational or irrational. \(f(x)=x^{3}-6 x^{2}+7 x+4\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4956, find all of the real zeros of the function, finding exact values whenever possible. Identify each zero as rational or irrational. \(f(x)=x^{4}-3 x^{3}-6 x^{2}+6 x+8\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4956, find all of the real zeros of the function, finding exact values whenever possible. Identify each zero as rational or irrational. \(f(x)=x^{4}-x^{3}-7 x^{2}+5 x+10\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4956, find all of the real zeros of the function, finding exact values whenever possible. Identify each zero as rational or irrational. \(f(x)=2 x^{4}-7 x^{3}-2 x^{2}-7 x-4\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4956, find all of the real zeros of the function, finding exact values whenever possible. Identify each zero as rational or irrational. \(f(x)=3 x^{4}-2 x^{3}+3 x^{2}+x-2\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Setting Production Schedules The Sunspot Small Appliance Co. determines that the supply function for their EverCurl hair dryer is \(S(p)=6+0.001 p^{3}\) and that its demand function is \(D(p)=80-0.02 p^{2}\), where p is the price. Determine the price for which the supply equals the demand and the num

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Setting Production Schedules The Pentkon Camera Co. determines that the supply and demand functions for their 35 mm70 mm zoom lens are \(S(p)=200-p+0.000007 p^{4}\) and \(D(p)=1500-0.0004 p^{3}\), where p is the price. Determine the price for which the supply equals the demand and the number of zoom

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Find the remainder when \(x^{40}-3\) is divided by \(x+1\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Find the remainder when \(x^{63}-17\) is divided by \(x-1\).

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Let \(f(x)=x^{4}+2 x^{3}-11 x^{2}-13 x+38\) (a) Use the upper and lower bound tests to prove that all of the real zeros of lie on the interval \([-5,4]\) (b) Find all of the rational zeros of . (c) Factor \(f(x)\) using the rational zero(s) found in (b). (d) Approximate all of the ir

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Lewiss distance D from a motion detector is given by the data in Table 2.15. (a) Find a cubic regression model, and graph it together with a scatter plot of the data. (b) Use the cubic regression model to estimate how far Lewis is from the motion detector initially. (c) Use the cu

Precalculus: Graphical, Numerical, Algebraic 8th Edition
True or False The polynomial function \(f(x)\) has a factor \(x+2\) if and only if \(f(2)=0\). Justify your answer.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
True or False If \(f(x)=(x-1)\left(2 x^{2}-x+1\right)+3\), then the remainder when \(f(x)\) is divided by \(x-1\) is 3 . Justify your answer.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Multiple Choice Let be a polynomial function with \(f(3)=0\). Which of the following statements is not true? (A) \(x+3\) is a factor of \(f(x)\). (B) \(x-3\) is a factor of \(f(x)\). (C) \(x=3\) is a zero of \(f(x)\). (D) 3 is an x-intercept of \(f(x)\). (E) The remainder when

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Multiple Choice Let \(\text { Let } f(x)=2 x^{3}+7 x^{2}+2 x-3\). Which of the following is not a possible rational root of ? (A) -3 (B) -1 (C) 1 (D) 1/2 (E) 2/3

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Multiple Choice Let \(f(x)=(x+2)\left(x^{2}+x-1\right)-3\). Which of the following statements is not true? (A) The remainder when \(f(x)\) is divided by \(x+2\) is -3. (B) The remainder when \(f(x)\) is divided by \(x-2\) is -3. (C) The remainder when \(f(x)\) is divided by \(x^{2}+x-1\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Multiple Choice Let \(f(x)=\left(x^{2}+1\right)(x-2)+7\). Which of the following statements is not true? (A) The remainder when \(f(x)\) is divided by \(x^{2}+1\) is 7. (B) The remainder when \(f(x)\) is divided by \(x-2\) is 7. (C) \(f(2)=7\) (D) \(f(0)=5\) (E) does not have a r

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Archimedes Principle A spherical buoy has a radius of 1 m and a density one-fourth that of seawater. By Archimedes Principle, the weight of the displaced water will equal the weight of the buoy. Let \(x=\) the depth to which the buoy sinks. Let \(d=\) the density of seawater. Let \(r=\

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Archimedes Principle Using the scenario of Exercise 69, find the depth to which the buoy will sink if its density is one-fifth that of seawater.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Biological Research Stephanie, a biologist who does research for the poultry industry, models the population P of wild turkeys, t days after being left to reproduce, with the function \(P(t)=-0.00001 t^{3}+0.002 t^{2}+1.5 t+100\) (a) Graph the function \(y=P(t)\) for appropriate values of t.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Architectural Engineering Dave, an engineer at the Trumbauer Group, Inc., an architectural firm, completes structural specifications for a 172-ft-long steel beam, anchored at one end to a piling 20 ft above the ground. He knows that when a 200-lb object is placed d feet from the anchored end, the bea

Precalculus: Graphical, Numerical, Algebraic 8th Edition
A classic theorem, Descartes Rule of Signs, tells us about the number of positive and negative real zeros of a polynomial function, by looking at the polynomials variations in sign. A variation in sign occurs when consecutive coefficients (in standard form) have opposite signs. If \(f(x)=a_{n} x^

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Writing to Learn Graph each side of the Example 3 summary equation: \(f(x)=\frac{2 x^{3}-3 x^{2}-5 x-12}{x-3}\) and \(g(x)=2 x^{2}+3 x+4, \quad x \neq 3\) How are these functions related? Include a discussion of the domain and continuity of each function.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Writing to Learn Explain how to carry out the following division using synthetic division. Work through the steps with complete explanations. Interpret and check your result. \(\frac{4 x^{3}-5 x^{2}+3 x+1}{2 x-1}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Writing to Learn The figure shows a graph of \(f(x)=x^{4}+0.1 x^{3}-6.5 x^{2}+7.9 x-2.4\) Explain how to use a grapher to justify the statement. \(f(x)=x^{4}+0.1 x^{3}-6.5 x^{2}+7.9 x-2.4\) \(\approx(x+3.10)(x-0.5)(x-1.13)(x-1.37)\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
(a) Writing to Learn Write a paragraph that describes how the zeros of \(f(x)=(1 / 3) x^{3}+x^{2}+2 x-3\) are related to the zeros of \(g(x)=x^{3}+3 x^{2}+6 x-9\). In what ways does this example illustrate how the Rational Zeros Theorem can be applied to find the zeros of a polynomial with rational n

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Use the Rational Zeros Theorem to prove \(\sqrt{2}\) is irrational.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Group Activity Work in groups of three. Graph \(f(x)=x^{4}+x^{3}-8 x^{2}-2 x+7\) (a) Use grapher methods to find approximate real number zeros. (b) Identify a list of four linear factors whose product could be called an approximate factorization of \(f(x)\). (c) Discuss what graphical a