Review Exercises
Add and Subtract Polynomials
Determine the Degree of Polynomials
In the following exercises, determine the type of polynomial.
16x2−40x−25
−15
Add and Subtract Polynomials
In the following exercises, add or subtract the polynomials.
4p+11p
(4a2+9a−11)+(6a2−5a+10)
(y2−3y+12)+(5y2−9)
Find the sum of 8q3−27 and q2+6q−2.
In the following exercises, simplify.
17mn2−(−9mn2)+3mn2
2pq2−5p−3q2
(3p2−4p−9)+(5p2+14)
(7b2−4b+3)−(8b2−5b−7)
Find the difference of (z2−4z−12) and (3z2+2z−11)
(x3−2x2y)−(xy2−3y3)−(x2y−4xy2)
Evaluate a Polynomial Function for a Given Value of the Variable
In the following exercises, find the function values for each polynomial function.
For the function g(x)=15−16x2, find:
ⓐ g(−1) ⓑ g(0) ⓒ g(2)
A pair of glasses is dropped off a bridge 640 feet above a river. The polynomial function h(t)=−16t2+640 gives the height of the glasses t seconds after they were dropped. Find the height of the glasses when t=6.
A manufacturer of the latest soccer shoes has found that the revenue received from selling the shoes at a cost of p dollars each is given by the polynomial R(p)=−5p2+360p. Find the revenue received when p=110 dollars.
Add and Subtract Polynomial Functions
In the following exercises, find ⓐ (f + g)(x) ⓑ (f + g)(3) ⓒ (f − g)(x) ⓓ (f − g)(−2)
f(x)=4x3−3x2+x−1 and g(x)=8x3−1
Properties of Exponents and Scientific Notation
Simplify Expressions Using the Properties for Exponents
In the following exercises, simplify each expression using the properties for exponents.
2·26
x·x8
2822
n3n12
30
(14t)0
Use the Definition of a Negative Exponent
In the following exercises, simplify each expression.
6−2
5·2−4
y−5
1a−4
−5−3
−(12)−3
(59)−2
In the following exercises, simplify each expression using the Product Property.
(y4)3
(a10)y
r−5·r−4
(m5)−1
In the following exercises, simplify each expression using the Power Property.
(k−2)−3
b8b−2
In the following exercises, simplify each expression using the Product to a Power Property.
(−5ab)3
(−6x3)−2
In the following exercises, simplify each expression using the Quotient to a Power Property.
(35x)−2
(4p−3q2)2
In the following exercises, simplify each expression by applying several properties.
(−3a−2)4(2a4)2(−6a2)3
In the following exercises, write each number in scientific notation.
2.568
0.00814
In the following exercises, convert each number to decimal form.
3.75×10−1
In the following exercises, multiply or divide as indicated. Write your answer in decimal form.
(3×107)(2×10−4)
6×1092×10−1
Multiply Polynomials
Multiply Monomials
In the following exercises, multiply the monomials.
(−6p4)(9p)
(8x2y5)(7xy6)
Multiply a Polynomial by a Monomial
In the following exercises, multiply.
7(10−x)
−5y(125y3−1)
Multiply a Binomial by a Binomial
In the following exercises, multiply the binomials using:
ⓐ the Distributive Property ⓑ the FOIL method ⓒ the Vertical Method.
(a+5)(a+2)
(3x+1)(2x−7)
In the following exercises, multiply the binomials. Use any method.
(n+8)(n+1)
(5u−3)(u+8)
(p+4)(p+7)
(3c+1)(9c−4)
Multiply a Polynomial by a Polynomial
In the following exercises, multiply using ⓐ the Distributive Property ⓑ the Vertical Method.
(x+1)(x2−3x−21)
In the following exercises, multiply. Use either method.
(m+6)(m2−7m−30)
Multiply Special Products
In the following exercises, square each binomial using the Binomial Squares Pattern.
(2x−y)2
(8p3−3)2
In the following exercises, multiply each pair of conjugates using the Product of Conjugates.
(3y+5)(3y−5)
(a+23b)(a−23b)
(13a2−8b4)(13a2+8b4)
Divide Monomials
Divide Monomials
In the following exercises, divide the monomials.
−26a8÷(2a2)
−30x8−36x9
11u6v355u2v8
(42r2s4)(54rs2)(6rs3)(9s)
Divide a Polynomial by a Monomial
In the following exercises, divide each polynomial by the monomial
63x3y2−99x2y3−45x4y39x2y2
Divide Polynomials using Long Division
In the following exercises, divide each polynomial by the binomial.
(4x2−21x−18)÷(x−6)
(n3−2n2−6n+27)÷(n+3)
Divide Polynomials using Synthetic Division
In the following exercises, use synthetic Division to find the quotient and remainder.
x3−3x2−4x+12 is divided by x+2
x4+x2+6x−10 is divided by x+2
Divide Polynomial Functions
In the following exercises, divide.
For functions f(x)=x3+x2−7x+2 and g(x)=x−2, find ⓐ (fg)(x)
ⓑ (fg)(3)
Use the Remainder and Factor Theorem
In the following exercises, use the Remainder Theorem to find the remainder.
f(x)=2x3−6x−24 divided by x−3
In the following exercises, use the Factor Theorem to determine if x−c is a factor of the polynomial function.
Determine whether x−3 is a factor of x3−7x2+11x+3.