 12.5.1: In Exercises 110, evaluate the binomial coefficients.
 12.5.2: In Exercises 110, evaluate the binomial coefficients.
 12.5.3: In Exercises 110, evaluate the binomial coefficients.
 12.5.4: In Exercises 110, evaluate the binomial coefficients.
 12.5.5: In Exercises 110, evaluate the binomial coefficients.
 12.5.6: In Exercises 110, evaluate the binomial coefficients.
 12.5.7: In Exercises 110, evaluate the binomial coefficients.
 12.5.8: In Exercises 110, evaluate the binomial coefficients.
 12.5.9: In Exercises 110, evaluate the binomial coefficients.
 12.5.10: In Exercises 110, evaluate the binomial coefficients.
 12.5.11: In Exercises 1132, expand the expression using the binomial theorem.
 12.5.12: In Exercises 1132, expand the expression using the binomial theorem.
 12.5.13: In Exercises 1132, expand the expression using the binomial theorem.
 12.5.14: In Exercises 1132, expand the expression using the binomial theorem.
 12.5.15: In Exercises 1132, expand the expression using the binomial theorem.
 12.5.16: In Exercises 1132, expand the expression using the binomial theorem.
 12.5.17: In Exercises 1132, expand the expression using the binomial theorem.
 12.5.18: In Exercises 1132, expand the expression using the binomial theorem.
 12.5.19: In Exercises 1132, expand the expression using the binomial theorem.
 12.5.20: In Exercises 1132, expand the expression using the binomial theorem.
 12.5.21: In Exercises 1132, expand the expression using the binomial theorem.
 12.5.22: In Exercises 1132, expand the expression using the binomial theorem.
 12.5.23: In Exercises 1132, expand the expression using the binomial theorem.
 12.5.24: In Exercises 1132, expand the expression using the binomial theorem.
 12.5.25: In Exercises 1132, expand the expression using the binomial theorem.
 12.5.26: In Exercises 1132, expand the expression using the binomial theorem.
 12.5.27: In Exercises 1132, expand the expression using the binomial theorem.
 12.5.28: In Exercises 1132, expand the expression using the binomial theorem.
 12.5.29: In Exercises 1132, expand the expression using the binomial theorem.
 12.5.30: In Exercises 1132, expand the expression using the binomial theorem.
 12.5.31: In Exercises 1132, expand the expression using the binomial theorem.
 12.5.32: In Exercises 1132, expand the expression using the binomial theorem.
 12.5.33: In Exercises 3336, expand the expression using Pascals triangle.
 12.5.34: In Exercises 3336, expand the expression using Pascals triangle.
 12.5.35: In Exercises 3336, expand the expression using Pascals triangle.
 12.5.36: In Exercises 3336, expand the expression using Pascals triangle.
 12.5.37: In Exercises 3744, find the coefficient C of the term in the binomi...
 12.5.38: In Exercises 3744, find the coefficient C of the term in the binomi...
 12.5.39: In Exercises 3744, find the coefficient C of the term in the binomi...
 12.5.40: In Exercises 3744, find the coefficient C of the term in the binomi...
 12.5.41: In Exercises 3744, find the coefficient C of the term in the binomi...
 12.5.42: In Exercises 3744, find the coefficient C of the term in the binomi...
 12.5.43: In Exercises 3744, find the coefficient C of the term in the binomi...
 12.5.44: In Exercises 3744, find the coefficient C of the term in the binomi...
 12.5.45: In a state lottery in which six numbers are drawn from a possible 4...
 12.5.46: In a state lottery in which six numbers are drawn from a possible 6...
 12.5.47: With a deck of 52 cards, 5 cards are dealt in a game of poker. Ther...
 12.5.48: In the card game canasta, two decks of cards including the jokers a...
 12.5.49: Evaluate the expression Solution: Write out the binomial coefficien...
 12.5.50: Expand Solution: Write out with blanks. (x 2y) 4 x4 x3 y x2 y2 xy3 ...
 12.5.51: n Exercises 5154, determine whether each statement is true or false.
 12.5.52: n Exercises 5154, determine whether each statement is true or false.
 12.5.53: n Exercises 5154, determine whether each statement is true or false.
 12.5.54: n Exercises 5154, determine whether each statement is true or false.
 12.5.55: Show that a if 0 k n. n
 12.5.56: Show that if n is a positive integer, then: Hint: Let and use the b...
 12.5.57: With a graphing utility, plot and in the same viewing screen. What ...
 12.5.58: With a graphing utility, plot and What is the binomial
 12.5.59: With a graphing utility, plot and for What do you notice happening ...
 12.5.60: With a graphing utility, plot and for What do you notice happening ...
 12.5.61: With a graphing utility, plot and for What do you notice happening ...
 12.5.62: With a graphing utility, plot and for What do you notice happening ...
Solutions for Chapter 12.5: The Binomial Theorem
Full solutions for Algebra and Trigonometry,  3rd Edition
ISBN: 9780840068132
Solutions for Chapter 12.5: The Binomial Theorem
Get Full SolutionsThis textbook survival guide was created for the textbook: Algebra and Trigonometry,, edition: 3. Algebra and Trigonometry, was written by and is associated to the ISBN: 9780840068132. This expansive textbook survival guide covers the following chapters and their solutions. Since 62 problems in chapter 12.5: The Binomial Theorem have been answered, more than 45788 students have viewed full stepbystep solutions from this chapter. Chapter 12.5: The Binomial Theorem includes 62 full stepbystep solutions.

Arccotangent function
See Inverse cotangent function.

Cofunction identity
An identity that relates the sine, secant, or tangent to the cosine, cosecant, or cotangent, respectively

Cosine
The function y = cos x

Cubic
A degree 3 polynomial function

Derivative of ƒ
The function defined by ƒ'(x) = limh:0ƒ(x + h)  ƒ(x)h for all of x where the limit exists

Dot product
The number found when the corresponding components of two vectors are multiplied and then summed

equation of a quadratic function
ƒ(x) = ax 2 + bx + c(a ? 0)

Frequency
Reciprocal of the period of a sinusoid.

Gaussian curve
See Normal curve.

Histogram
A graph that visually represents the information in a frequency table using rectangular areas proportional to the frequencies.

Lower bound of f
Any number b for which b < ƒ(x) for all x in the domain of ƒ

nth power of a
The number with n factors of a , where n is the exponent and a is the base.

Ordinary annuity
An annuity in which deposits are made at the same time interest is posted.

Power regression
A procedure for fitting a curve y = a . x b to a set of data.

Real axis
See Complex plane.

Relevant domain
The portion of the domain applicable to the situation being modeled.

Second quartile
See Quartile.

Sinusoid
A function that can be written in the form f(x) = a sin (b (x  h)) + k or f(x) = a cos (b(x  h)) + k. The number a is the amplitude, and the number h is the phase shift.

Standard unit vectors
In the plane i = <1, 0> and j = <0,1>; in space i = <1,0,0>, j = <0,1,0> k = <0,0,1>

Upper bound for real zeros
A number d is an upper bound for the set of real zeros of ƒ if ƒ(x) ? 0 whenever x > d.