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# 9.9: Chapter 9 Review

Difficulty Level: At Grade Created by: CK-12

Define the following words:

1. Polynomial
2. Monomial
3. Trinomial
4. Binomial
5. Coefficient
6. Independent events
7. Factors
8. Factoring
9. Greatest common factor
10. Constant
11. Mutually exclusive
12. Dependent events

Identify the coefficients, constants, and the polynomial degrees in each of the following polynomials.

1. x53x3+4x25x+7\begin{align*}x^5-3x^3+4x^2-5x+7\end{align*}
2. x43x3y2+8x12\begin{align*}x^4-3x^3y^2+8x-12\end{align*}

Rewrite the following in standard form.

1. 4b+4+b2\begin{align*}-4b+4+b^2\end{align*}
2. 3x2+5x42x+9\begin{align*}3x^2+5x^4-2x+9\end{align*}

Add or subtract the following polynomials and simplify.

1. Add x22xy+y2\begin{align*}x^2-2xy+y^2\end{align*} and 2y24x2\begin{align*}2y^2-4x^2\end{align*} and 10xy+y3\begin{align*}10xy+y^3\end{align*}.
2. Subtract x33x2+8x+12\begin{align*}x^3-3x^2+8x+12\end{align*} from 4x2+5x9\begin{align*}4x^2+5x-9\end{align*}.
3. Add 2x3+3x2y+2y\begin{align*}2x^3+3x^2 y+2y\end{align*} and x32x2y+3y\begin{align*}x^3-2x^2 y+3y\end{align*}

Multiply and simplify the following polynomials.

1. (3y4)(2y2)\begin{align*}(-3y^4)(2y^2)\end{align*}
2. 7a2bc3(5a23b29c2)\begin{align*}-7a^2bc^3(5a^2-3b^2-9c^2)\end{align*}
3. 7y(4y22y+1)\begin{align*}-7y(4y^2-2y+1)\end{align*}
4. (3x2+2x5)(2x3)\begin{align*}(3x^2+2x-5)(2x-3)\end{align*}
5. (x29)(4x4+5x22)\begin{align*}(x^2-9)(4x^4+5x^2-2)\end{align*}
6. (2x3+7)(2x37)\begin{align*}(2x^3+7)(2x^3-7)\end{align*}

Square the binomials and simplify.

1. (x2+4)2\begin{align*}(x^2+4)^2\end{align*}
2. (5x2y)2\begin{align*}(5x-2y)^2\end{align*}
3. (13x2+2y)\begin{align*}(13x^2+2y)\end{align*}

Solve the following polynomial equations.

1. 4x(x+6)(4x9)=0\begin{align*}4x(x+6)(4x-9)=0\end{align*}
2. x(5x4)=0\begin{align*}x(5x-4)=0\end{align*}

Factor out the greatest common factor of each expression

1. 12n+28n+4\begin{align*}-12n+28n+4\end{align*}
2. 45x10+45x7+18x4\begin{align*}45x^{10}+45x^7+18x^4\end{align*}
3. 16y58y5x2+40y6x3\begin{align*}-16y^5-8y^5 x^2+40y^6 x^3\end{align*}
4. 15u410u610u3v\begin{align*}15u^4-10u^6-10u^3 v\end{align*}
5. 6a9+20a4b+10a3\begin{align*}-6a^9+20a^4 b+10a^3\end{align*}
6. 12x+27y227x6\begin{align*}12x+27y^2-27x^6\end{align*}

Factor the difference of squares.

1. x2100\begin{align*}x^2-100\end{align*}
2. x21\begin{align*}x^2-1\end{align*}
3. 16x225\begin{align*}16x^2-25\end{align*}
4. 4x281\begin{align*}4x^2-81\end{align*}

Factor the following expressions completely.

1. 5n2+25n\begin{align*}5n^2+25n\end{align*}
2. 7r2+37r+36\begin{align*}7r^2+37r+36\end{align*}
3. 4v2+36v\begin{align*}4v^2+36v\end{align*}
4. 336xy288x2+294y252x\begin{align*}336xy-288x^2+294y-252x\end{align*}
5. 10xy25x+8y20\begin{align*}10xy-25x+8y-20\end{align*}

Complete the following problems.

1. 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.
2. A rectangle has sides of x+5\begin{align*}x+5\end{align*} and x3\begin{align*}x-3\end{align*}. What value of x\begin{align*}x\end{align*} gives an area of 48?
3. 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”
4. You spin a spinner with seven equal sections numbered one through seven and roll a six-sided cube. What is the probability that you roll a five on both the cube and the spinner?
5. You spin a spinner with seven equal sections numbered one through seven and roll a six-sided cube. Are these eventually mutually exclusive?
6. You spin a spinner with seven equal sections numbered one through seven and roll a six-sided cube. Are these events independent?
7. You spin a spinner with seven equal sections numbered one through seven and roll a six-sided 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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CK.MAT.ENG.SE.1.Algebra-Basic.9.9