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1001 Algebra II Practice Problems For Dummies
book

1001 Algebra II Practice Problems For Dummies

by Mary Jane Sterling
June 2013
Beginner content levelBeginner
504 pages
9h 8m
English
For Dummies
Content preview from 1001 Algebra II Practice Problems For Dummies

Chapter 18

The Answers

1.    8x2 + 8x – 6

Apply “FOIL” to multiply the terms in the binomials.

First: 2x(4x) = 8x2

Outer: 2x(–2) = –4x

Inner: 3(4x) = 12x

Last: 3(–2) = –6

Combine these products and simplify:

8x2 – 4x + 12x – 6 = 8x2 + 8x – 6

2.    4x2 + 3x – 4

First, multiply the two binomials together using “FOIL.”

(x + 4)(x – 1) = x2x + 4x – 4 = x2 + 3x – 4

Now add 3x2 to that product.

3x2 + x2 + 3x – 4 = 4x2 + 3x – 4

3.    8x2 – 2x – 11

First, perform the two multiplications.

(3x + 1)(x – 3) = 3x2 – 9x + x – 3 = 3x2 – 8x – 3

(x + 2)(5x – 4) = 5x2 – 4x + 10x – 8 = 5x2 + 6x – 8

Then add the two products.

3x2 – 8x – 3 + 5x2 + 6x – 8 = 8x2 – 2x – 11

4.    8x2 – 20x – 11

First, perform the two multiplications.

5(x – 3)(x + 2) = 5(x2x – 6) = 5x2 – 5x – 30

3(x – 3)(x – 2) = 3(x2 – 5x + 6) = 3x2 – 15x + 18

Then add the two products and the 1.

5x2 – 5x – 30 + 3x2 – 15x + 18 + 1 = 8x2 – 20x – 11

5.    x3 + x2 – 7x + 20

Distribute the two terms in the binomial over the terms in the trinomial; then combine like terms.

x(x2 – 3x + 5) + 4(x2 – 3x + 5)

= x3 – 3x2 + 5x + 4x2 – 12x + 20

= x3 + x2 – 7x + 20

6.    3x3x2 – 3x + 1

Distribute the two terms in the binomial over the terms in the trinomial; then combine like terms.

x(3x2 + 2x – 1) – 1(3x2 + 2x – 1)

= 3x3 + 2x2x – 3x2 – 2x + 1

= 3x3x2 – 3x + 1

7.    2x3 + 3x2 – 23x – 12

First, multiply the second and third binomials together.

(2x + 1)(x – 3)(x + 4) =

(2x + 1)(x2 + x – 12)

Now distribute the two terms in the binomial ...

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Publisher Resources

ISBN: 9781118446614Publisher Support