Question

Please can you help me create a factorable polynomial with a GCF of 7. Then rewrite that same polynomial in two equivalent forms. Please explain how each form was created. Thank you!

Answer 1

Polynomial: 7x² + 21x + 14

Equivalent forms: 7(x² + 3x + 2) or 7(x + 1)(x + 2)

Step-by-step explanation:

A factorable polynomial with GCF of 7 can be created as 7 times some factors, so

7(x + 1)(x + 2)

7(x(x) + x(2) + 1(x) + 1(2))

7(x² + 2x + x + 2)

7(x² + 3x + 2)

7(x²) + 7(3x) + 7(2)

7x² + 21x + 14

Therefore, a factorable polynomial with a GCD of 7 is

7x² + 21x + 14

Additionally, it can be written as

7(x² + 3x + 2) or

7(x + 1)(x +2)