MATH 1100 Week Two
MATH 1100 Week Two MATH 1100.140
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This 7 page Class Notes was uploaded by Kait Brown on Monday September 12, 2016. The Class Notes belongs to MATH 1100.140 at University of North Texas taught by Mary Ann Barber in Fall 2016. Since its upload, it has received 7 views. For similar materials see College Algebra in Math at University of North Texas.
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Date Created: 09/12/16
W eekly Notes Math 1100.140,84 0 College Algebra Week two Unit One P.3 Polynomials (Continued) p.4 Factoring Polynomials 1.1 Equations and inequalities P.3.4. Find the product -6y(2y+5) *6y *6y 1. Multiply 6y through the equation -12y -30y P.3.5. Find the product (x+3)(x +6x+7) 2 2 (x(x +6x+7)) + (3(x +6x+7) 1. Reset equation. We want to multiply each part of the binomial by each part of the trinomial. (x +6x +7x)+(3x +18x+21) 2. Multiply x by the binomial and 3 by the binomial x +9x +25x+21 3. Add like terms P.3.6. Simplify 2 2 (2x-1) -4x 2 (2x-1)(2x-1)-4x 1. Reset equation 2 2 (4x -2x-2x+1)-4x 2. Multiply (2x-1)(2x-1) (4x -2x-2x+1)-4x -4x+1 3. Combine like terms and simplify P.3.7. Multiply out the following: A) 2 2 (x+5)(x+5) (x +5x+5x+25) x +10x+25 B) 2 2 (x-5)(x-5) (x -5x-5x+25) x -10x+25 C) 2 2 (x+5)(x-5) x -5x+5x-25 x -25 P.3.8 Multiply out the following and simplify: A) (x+2) 3 (x+2)(x+2)(x+2) 1. Reset equation (x +2x+2x+4) 2. Multiply TWO binomials 2 (x+2)(x +4x+4) 3. Multiply last binomial into solution from step 2. 2 2 3 2 2 (x(x +4x+4))+(2(x +4x+4)) (x +4x +4x)+(2x +8x+8) x +6x +12x+8 4. Combine like terms. B)(x-2) 3 (x-2)(x-2)(x-2) 1. Reset equation 2 (x -2x-2x+4) 2. Multiply TWO binomials 2 (x-2)(x -4x+4) 3. Multiply last binomial into the solution from step 2. (x(x -4x+4))-(2(x -4x+4)) (x -4x +4x)-(2x -8x+8) x -6x +12x-8 4. Combine like terms. **Remember, when we’re subtracting polynomials, the signs can get confusing. Personally, it’s easier to switch all the signs on paper 3 before I start combining anything. So instead of working with (x - 4x +4x)-(2x -8x+8), I’m working with x -4x +4x-2x +8x-8. If I skip this step, or try to do it in my head, I always mess the entire thing up and have to start all over, convinced that I made an error in the very beginning. Don’t be like me. Be smart. 2 C) (x+4)(x -4x+16) 2 2 (x(x -4x+16)+(4(x -4x+16) 1. Multiply each term of the binomial in the trinomial (x -4x +16x)+(4x -16x+64) 2. Combine the resulting trinomials 3 2 2 3 x -4x +16x+4x -16x+64 x +64 3. Combine like terms to simplify D)(x-4)(x +4x+16) (x(x +4x+16)-(4(x +4x+16) 1. Multiply each term of the binomial in the trinomial 3 2 2 (x +4x +16x)-(4x +16x+64) 2. Combine the resulting trinomials 3 2 2 3 x +4x +16x-4x -16x+64 x -643. Combine like terms to simplify P.6 P.6.4 3 y Find (x ) 3 y 3y (x ) =x P.6.5 If (x ) =x, what is y? Facts that we know: (x ) =x =x 1 So what can you multiply by 3 to equal 1? x3(1/=x =x y=1/3 P.6.6 3 3 Describe in words, then find √x Cubed root of x raised to the power of 3. 3 3 3 1/3 1 √x =(x ) =x =x P.6.8 Simplify the following: A) √-64=No real root B) √-125=-5 (16/625)1/4 161/4 2 1/4 625 = 5 Simplify the incomplete problems below: √27= √300= 1. Factor the integer using a factor which is a perfect square √9*√3 √100*√3 2. Unsquare the perfect square. 3*√3 10*√3 6.10 Simplify the radical √(5/18) √5 1. Rewrite the radical with √ on the numerator and the √18 denominator √5 √9*√2 2. Factor denominator using perfect square √5 3*√2 3. Factor perfect square 4. Because we are dividing by √2, we want to multiply each side √5 * √2by √2, then simplify P.6.11 Simplify the radical 3 √(7/5) 3√7 * 3√5 2 = 3√(7*25) 1. Reset the fraction and cross multiply 2 by √5 (to even out) 3√5 * 3√5 = 3√53 3√175 2. Simplify 5 Introduction to Chapter 1: Difference of Squares: a -b =(a-b)(a+b) Zero Product Property: ab=0; a, b=0 1.1 Linear Equations are first-degree equations in one variable that contain the equality symbol, “=”. Linear equation in the variable x can be expresses in the standard form, ax+b=c, where a ≠, b ∊ ℝ The domain is the largest set of acceptable input values. Of note, the denominator of a fraction cannot be equal to zero. 1.1.1 Solve ax+b=0, solve for x ax+(b-b)=(0-b) 1. Isolate x by subtracting b from both sides. x/a=-b/a 2. Divide both sides by a x=-b/a 1.1.2 Solve 5x-3=2x+8 -2x -2x 1. Subtract 2x from each side 3x-3=8 +3 +3 2. Add 3 to each side 3x=11 /3 /3 3. Divide each side by 3 x=11/3 1.1.3 Solve 400t-85=11-50t +50t +50t 1. Add 50t to each side 450t-85=11 +85 +85 2. Add 85 to each side 450t=96 /450 /450 3. Divide each side by 450 t=16/75
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