Question

Create a factorable polynomial with a GCF of 2y. Rewrite that polynomial in two other equivalent forms. Explain how each form was created.

Answer 1

Create a factorable polynomial with a GCF of 3x. Rewrite that polynomial in two other equivalent forms. Explain how each form was created. (10 points)

My answer:

6x^3 + 39x^2 + 60x

two other equivalent forms:

1. 3x(x+4)(5+2x)

2. 3x(2x^2 + 13x +20)

1st- Here's how I got the first equation. I just choose 2 random binomial factors off the top of my head and had them be multiplied with 3x since it's the GCF.

2nd- Here's how I got the second equation. Using the last equation, 3x(x+4)(5+2x), I just multiplied (x+4) with (5+2x) which equals 2x^2 + 13x + 20.

Explanation:

I actually got help from my teacher for this so I know it's right. Really hope this helps because I was also having trouble with this :)

Answer 2

The GCF of a polynomial is the greatest factor which is common to all the terms of the polynomial.

Thus, an example of a polynomial with a GCF of 2y is

`6y^3-12y^2+4y`

The above polynomial can also be rewritten as

`2y(3y^2-6y+2)`

This form of the polynomial is obtained by factoring out the GCF of the polynomial.