Question

Create a favorable polynomial with a GCF of 5z. Rewrite the polynomial in two other equivalent forms. EXPLAIN how each form was created!

PLEASE SHOW ALL WORK!

Answer 1

Start by multiplying 5z by the sum of two terms, then 5z will definitely be factorable. 5z⋅2z+5z⋅7Multiply it out to get 10z2+35z
The GCF of 10 and 35 is 5.
The GCF of z2 and z is z.
Therefore the GCF of the new binomial above is 5z

Answer 2

Answer & Step-by-step explanation:

Start by multiplying 5z by a non-factorable polynomial. This will keep it as the greatest common factor.  

5z(z + 1) = 5z^2 + 5z

Then you can multiply or divide both the numerator and denominator by the same value to keep it equivalent.

Equivalent form 1: [(5z^2 + 5z)(Z - 1)] / (z-1) = [5z^3 + 5z^2 - 5z^2 - 5z] / (z-1) = (5z^3 - 5z) / (z-1)

Equivalent form 2: [(5z^2 + 5z) / z^2] (z^2) = (5 + 5/z)(z^2)