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 ...
