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Chapter 5 Review

Write polynomials in standard form and name them based on degree and number of terms

1. 4b + b + 2 2. 6x3 ( 1 3. 1 ( 2s + 5s4

A2.A.7 Factor polynomial expressions completely, using any combination of the following

techniques: common factor extraction, difference of two perfect squares, quadratic

trinomials

A2.A.26 Find the solution to polynomial equations of higher degree that can be solve using

factoring and/or the quadratic formula

Basic Factoring (Re-write in proper order then do a*c to get the number you need factors of )

1. Factor: 12x2 + 2 + 11x

2. Factor: 4a2 + 11a – 20

Factoring by GCF

1. Solve the equation 2x3 – 5x2 = 3x algebraically for all values of x.

Factoring by grouping

1. Factor x3 + 2x2 – 3x – 6

Factoring by replacing x2 with a

1. Solve, giving 4 roots, x4 – 13x2 + 36 = 0

2. Solve for the real roots, x4 – 9x2 + 14

Difference of Perfect Squares

1. Factor: x8 – 16

2. Factor: 16a4 – b8

Factoring Perfect Square Trinomials

1. Factor 4a2 – 12a + 9

2. Factor 16x2 + 40x + 25

A2.A.50 Finding roots to higher degree polynomials, by inspecting a graph

(Find the x –intercepts)

Find the real solutions of each equation by graphing.

1. 36x3 + 6x2 = 9x solutions are:____________________________

2. The graph of y = x3 – 4x2 + x + 6 is shown below.

[pic]

What is the product of the roots of the equation x3 – 4x2 + x + 6 = 0 ?

1) -36 2) -6 3) 6 4) 4

A2.A.36 Pascal’s Triangle and Binomial Theorem

[pic]

1. Use Pascal’s Triangle to Expand the following Binomial: (3a − b)3

[pic]

C represents a probability combination and you use your graphing calculator to find it.

• Notice that 1st term is nC0 , so the number after the C is one less than the term you are looking for

______1. What is the fifth term in the expansion of [pic]?

|1) |[pic] |

|2) |[pic] |

|3) |[pic] |

|4) |[pic] |

_______2. What is the coefficient of the fifth term in the expansion of [pic]?

1) 8 2) 28 3) 56 4) 70

______3. What is the coefficient of the fourth term in the expansion of [pic]?

1)  -5,376 2)  -336 3)  336 4)  5,376

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[pic]

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