Question

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

Answer 1

Answer:

Part 1)

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

Part 2)

$(2x^3-10x^2+5x+14)\div(x-2)=2x^2-6x-7$

Step-by-step 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:

$(2x^3-10x^2+5x+14)\div(x-2)$

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:

$(2x^3-10x^2+5x+14)\div(x-2)=2x^2-6x-7$