Question

5a^2-25a Select the method(s) of factoring that must be used to factor the following polynomial (select all that apply): Difference of Squares, Product Sum Factoring, Greatest Common Factor (GCF), Bottoms Up Factoring, Cannot be factored.

Answer 1

We are given : 5a^2-25a

Please note: We always check Greatest Common Factor (GCF) first when factoring a polynomial.

If Greatest Common Factor (GCF) exist we factor out GCF.

In the given polynomial, we can see that greatest common factor of 5a^2 and 25a is 5a.

So, we would factor out GCF 5a first.

In order to factor out GCF, we need to divide all terms of the polynomila by GCF we got.

If we factor out 5a from 5a^2 -25a, we need to divide 5a^2 and -25a by 5a.

On dividing 5a^2 by 5a we get a and

on dividing -25a by 5a we get -5.

Therefore, on factoring out 5a, we get

5a(a-5).

Therefore, we use Greatest Common Factor (GCF) method of factoring.