9.9: Chapter 9 Review
Difficulty Level: At Grade
Created by: CK12
Define the following words:
 Polynomial
 Monomial
 Trinomial
 Binomial
 Coefficient
 Independent events
 Factors
 Factoring
 Greatest common factor
 Constant
 Mutually exclusive
 Dependent events
Identify the coefficients, constants, and the polynomial degrees in each of the following polynomials.

x5−3x3+4x2−5x+7 
x4−3x3y2+8x−12
Rewrite the following in standard form.

−4b+4+b2 
3x2+5x4−2x+9
Add or subtract the following polynomials and simplify.
 Add
x2−2xy+y2 and2y2−4x2 and10xy+y3 .  Subtract
x3−3x2+8x+12 from4x2+5x−9 .  Add
2x3+3x2y+2y andx3−2x2y+3y
Multiply and simplify the following polynomials.

(−3y4)(2y2) 
−7a2bc3(5a2−3b2−9c2) 
−7y(4y2−2y+1) 
(3x2+2x−5)(2x−3) 
(x2−9)(4x4+5x2−2) 
(2x3+7)(2x3−7)
Square the binomials and simplify.

(x2+4)2 
(5x−2y)2 
(13x2+2y)
Solve the following polynomial equations.

4x(x+6)(4x−9)=0 
x(5x−4)=0
Factor out the greatest common factor of each expression

−12n+28n+4 
45x10+45x7+18x4 
−16y5−8y5x2+40y6x3 
15u4−10u6−10u3v 
−6a9+20a4b+10a3 
12x+27y2−27x6
Factor the difference of squares.

x2−100 
x2−1 
16x2−25 
4x2−81
Factor the following expressions completely.

5n2+25n 
7r2+37r+36 
4v2+36v 
336xy−288x2+294y−252x 
10xy−25x+8y−20
Complete the following problems.
 One leg of a right triangle is 3 feet longer than the other leg. The hypotenuse is 15 feet. Find the dimensions of the right triangle.
 A rectangle has sides of
x+5 andx−3 . What value ofx gives an area of 48?  Are these two events mutually exclusive, mutually inclusive, or neither? “Choosing the sports section from a newspaper” and “choosing the times list for the movie theatre”
 You spin a spinner with seven equal sections numbered one through seven and roll a sixsided cube. What is the probability that you roll a five on both the cube and the spinner?
 You spin a spinner with seven equal sections numbered one through seven and roll a sixsided cube. Are these eventually mutually exclusive?
 You spin a spinner with seven equal sections numbered one through seven and roll a sixsided cube. Are these events independent?
 You spin a spinner with seven equal sections numbered one through seven and roll a sixsided cube. What is the probability you spin a 3, 4, or 5 on the spinner or roll a 2 on the cube?
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Date Created:
Feb 22, 2012Last Modified:
Dec 11, 2014
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