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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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