Question

Create a factorable polynomial with a GCF of 5z. Rewrite that polynomial in two other equivalent forms. Explain how each form was created.

Answer 1

Answer with explanation:

It is given that, G C F of two polynomials is 5 z.

We have to Write that two polynomials.

A=5 z² + 5 z =5× z× (z+1)

B=10 z + 5 z²=5×z×(z+2)

→→G C F ,of A and B=5 z

Now, writing polynomials in equivalent form

1.5 z² + 5 z =5× z× (z+1)=(z+1)×z×5=5 z + z²

2. 10 z + 5 z²=5×z×(z+2)=(z+2)×z×5=5 z² + 10 z

to write in equivalent form of above polynomials, we have used commutative property of addition ,and Multiplication ,which states that, A+B=B +A, and AB=BA.

And, Distributive property of multiplication with respect to addition and Subtraction.

1. A × (B +C)=A × B + A × C

2. A × (B -C)=A × B - A × C