Question

Create your own factorable polynomial with a GCF of 7. Rewrite that polynomial in two other equivalent forms. Explain how each form was created

Answer 1

Factorable polynomial with a GCF of 7: 7x^2 + 14x + 21
Equivalent forms: x^2 + 2x + 3 OR 14x^2 + 28x + 42.
The first equivalent form was created by dividing each term by 7, and the second equivalent form was created by multiplying each term by 2.

Answer 2

Answer with step-by-step explanation:

The polynomial with a greatest common factor (GCF) 7 is written as:

                       7x²+14x+21.

( since, gcd{7,14,21}=7)

Now, Equivalent expression of a polynomial means that it could be represented in some other way but at every point it must give the same value as the original polynomial.

The equivalent expression for the above polynomial is:

1)   7(x²+2x+3)

since, we took 7 common from all the three terms.

2)  7x(x+2)+21

Here we took 7x common from first two terms and  wrote the remaining polynomial terms as it is.