Question

Create a factorable polynomial with a GCF of 7. Rewrite that polynomial in two other equivalent forms. Explain how each form was created. (10 points)

Answer 1

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 7 is

The above polynomial can also be rewritten as

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

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 7 is :

21x^2-42x+14

The above polynomial can also be rewritten as

7(3x^2-6x+2)

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