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) = x2 – x + 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(x2 – x – 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. 3x3 – x2 – 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 + 2x2 – x – 3x2 – 2x + 1

= 3x3 – x2 – 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 ...