Question

HELP. Multiply the polynomials and simplify the answer. Show your work.

(3a³ - 2a - 7) and (4a² - 2a + 1)

Simplify the expression using long division. Show your work.
(2x³ - 10x² + 5x +14) ÷ (x-2)

Answer 1

Part 1)

`=12a^5-6a^4-5a^3-24a^2+12a-7`

Part 2)

`(2x^3-10x^2+5x+14)/(x-2)=2x^2-6x-7`

Explanation:

Part 1)

We would like to multiply:

`(3a^3-2a-7)(4a^2-2a+1)`

Distribute each term from the first group into the second group. So:

`=3a^3(4a^2-2a+1)-2a(4a^2-2a+1)-7(4a^2-2a+1)`

Distribute further:

`=(12a^5-6a^4+3a^3)+(-8a^3+4a^2-2a)+(-28a^2+14a-7)`

Combine like terms:

`=(12a^5)+(-6a^4)+(3a^3-8a^3)+(-28a^2+4a^2)+(-2a+14a)+(-7)`

Simplify:

`=12a^5-6a^4-5a^3-24a^2+12a-7`

Part 2)

We would like to divide:

`(2x^3-10x^2+5x+14)/(x-2)`

Using long division.

Please refer to the attached document.

For the first step, x goes into 2x³ 2x² times. Hence, we multiply our divisor by 2x².

Next, x goes into -6x^2 -6x times. Hence, we multiply our divisor by -6x.

Finally, x goes into -7x -7 times. So, we multiply our divisor by -7 and we simplify.

Therefore:

`(2x^3-10x^2+5x+14)/(x-2)=2x^2-6x-7`