10.9.1: Review Exercises
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Review Exercises
Add and Subtract Polynomials
Identify Polynomials, Monomials, Binomials and Trinomials
In the following exercises, determine if each of the following polynomials is a monomial, binomial, trinomial, or other polynomial.
y2+8y−20
−6a4
9x3−1
n3−3n2+3n−1
Determine the Degree of Polynomials
In the following exercises, determine the degree of each polynomial.
16x2−40x−25
5m+9
−15
y2+6y3+9y4
Add and Subtract Monomials
In the following exercises, add or subtract the monomials.
4p+11p
−8y3−5y3
Add 4n5,−n5,−
Subtract 10x2 from 3x2
Add and Subtract Polynomials
In the following exercises, add or subtract the polynomials.
(4a2+9a−11)+(6a2−5a+10)
(8m2+12m−5)−(2m2−7m−1)
(y2−3y+12)+(5y2−9)
(5u2+8u)−(4u−7)
Find the sum of 8q3−27 and q2+6q−2
Find the difference of x2+6x+8 and x2−8x+15
Evaluate a Polynomial for a Given Value of the Variable
In the following exercises, evaluate each polynomial for the given value.
200x−15x2 when x=5
200x−15x2 when x=0
200x−15x2 when x=15
5+40x−12x2 when x=10
5+40x−12x2 when x=−4
5+40x−12x2 when x=0
A pair of glasses is dropped off a bridge 640 feet above a river. The polynomial −16t2+640 gives the height of the glasses t seconds after they were dropped. Find the height of the glasses when t=6.
The fuel efficiency (in miles per gallon) of a bus going at a speed of x miles per hour is given by the polynomial −1160x2+12x. Find the fuel efficiency when x=20 mph.
Use Multiplication Properties of Exponents
Simplify Expressions with Exponents
In the following exercises, simplify.
63
(12)4
(−0.5)2
−32
Simplify Expressions Using the Product Property of Exponents
In the following exercises, simplify each expression.
p3·p10
2·26
a·a2·a3
x·x8
Simplify Expressions Using the Power Property of Exponents
In the following exercises, simplify each expression.
(y4)3
(r3)2
(32)5
(a10)y
Simplify Expressions Using the Product to a Power Property
In the following exercises, simplify each expression.
(8n)2
(−5x)3
(2ab)8
(−10mnp)4
Simplify Expressions by Applying Several Properties
In the following exercises, simplify each expression.
(3a5)3
(4y)2(8y)
(x3)5(x2)3
(5st2)3(2s3t4)2
Multiply Monomials
In the following exercises, multiply the monomials.
(−6p4)(9p)
(13c2)(30c8)
(8x2y5)(7xy6)
(23m3n6)(16m4n4)
Multiply Polynomials
Multiply a Polynomial by a Monomial
In the following exercises, multiply.
7(10−x)
a2(a2−9a−36)
−5y(125y3−1)
(4n−5)(2n3)
Multiply a Binomial by a Binomial
In the following exercises, multiply the binomials using various methods.
(a+5)(a+2)
(y−4)(y+12)
(3x+1)(2x−7)
(6p−11)(3p−10)
(n+8)(n+1)
(k+6)(k−9)
(5u−3)(u+8)
(2y−9)(5y−7)
(p+4)(p+7)
(x−8)(x+9)
(3c+1)(9c−4)
(10a−1)(3a−3)
Multiply a Trinomial by a Binomial
In the following exercises, multiply using any method.
(x+1)(x2−3x−21)
(5b−2)(3b2+b−9)
(m+6)(m2−7m−30)
(4y−1)(6y2−12y+5)
Divide Monomials
Simplify Expressions Using the Quotient Property of Exponents
In the following exercises, simplify.
2822
a6a
n3n12
xx5
Simplify Expressions with Zero Exponents
In the following exercises, simplify.
30
y0
(14t)0
12a0−15b0
Simplify Expressions Using the Quotient to a Power Property
In the following exercises, simplify.
(35)2
(x2)5
(5mn)3
(s10t)2
Simplify Expressions by Applying Several Properties
In the following exercises, simplify.
(a3)2a4
u3u2·u4
(xx9)5
(p4·p5p3)2
(n5)3(n2)8
(5s24t)3
Divide Monomials
In the following exercises, divide the monomials.
72p12÷8p3
−26a8÷(2a2)
45y6−15y10
−30x8−36x9
28a9b7a4b3
11u6v355u2v8
(5m9n3)(8m3n2)(10mn4)(m2n5)
42r2s46rs3−54rs29s
Integer Exponents and Scientific Notation
Use the Definition of a Negative Exponent
In the following exercises, simplify.
6−2
(−10)−3
5·2−4
(8n)−1
Simplify Expressions with Integer Exponents
In the following exercises, simplify.
x−3·x9
r−5·r−4
(uv−3)(u−4v−2)
(m5)−1
(k−2)−3
q4q20
b8b−2
n−3n−5
Convert from Decimal Notation to Scientific Notation
In the following exercises, write each number in scientific notation.
5,300,000
0.00814
The thickness of a piece of paper is about 0.097 millimeter.
According to www.cleanair.com, U.S. businesses use about 21,000,000 tons of paper per year.
Convert Scientific Notation to Decimal Form
In the following exercises, convert each number to decimal form.
2.9×104
1.5×108
3.75×10−1
9.413×10−5
Multiply and Divide Using Scientific Notation
In the following exercises, multiply and write your answer in decimal form.
(3×107)(2×10−4)
(1.5×10−3)(4.8×10−1)
6×1092×10−1
9×10−31×10−6
Introduction to Factoring Polynomials
Find the Greatest Common Factor of Two or More Expressions
In the following exercises, find the greatest common factor.
5n,45
8a,72
12x2,20x3,36x4
9y4,21y5,15y6
Factor the Greatest Common Factor from a Polynomial
In the following exercises, factor the greatest common factor from each polynomial.
16u−24
15r+35
6p2+6p
10c2−10c
−9a5−9a3
−7x8−28x3
5y2−55y+45
2q5−16q3+30q2