Question

Question 4 (Essay Worth 10 points)

Answer 1

As the GCF is 3x let us write a polynomial and then multiply it by 3x.

Here is a polynomial: $x^{2} +5x-1$

If we multiply it by 3x we get $(3x)( x^{2} +5x-1)$. Since we have a product (two expressions being multiplied together) this is factored. So this is the factored form of the polynomial we created with GCF of 3x.

Let’s multiply the terms in the parenthesis by 3x to get the same polynomial but written a different way:
$3 x^{3}+15 x^{2} -3x$. This is the factorable polynomial and the one we had before is the factored polynomial (also an equivalent form)

To get another equivalent form I could multiply out only the first term. This gives us $3 x^{3}+3x(5x-1)$ another equivalent form.