O'Reilly logo

1001 Algebra II Practice Problems For Dummies by Mary Jane Sterling

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

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 ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required