Question

Hello I have a practice test that I can take multiple times until I get it right and I have been stuck on a problem

Answer 1

The answers are Options A and B

EXPLANATION :

From the problem, we have :

`(4x^3+4x-6)(-4x^2+x-3)`

We can distribute each term of the first parenthesis to the second parenthesis :

`\begin{gathered} 4x^3(-4x^2+x-3)+4x(-4x^2+x-3)-6(-4x^2+x-3) \\ =(-16x^5+4x^4-12x^3)+(-16x^3+4x^2-12x)-(-24x^2+6x-18) \\ \\ \text{ Combine like terms :} \\ \\ =-16x^5+4x^4-12x^3-16x^3+4x^2+24x^2-12x-6x+18 \\ =-16x^5+4x^4-28x^3+28x^2-18x+18 \end{gathered}`

And we can also group two consecutive terms :

`\begin{gathered} (-16x^5+4x^4)+(-28x^3+28x^2)+(-18x+18) \\ =-4(4x^5-4x^4)-28(x^3-x^2)-18(x-1) \end{gathered}`