Question

When factoring 16x2 -

36, what is the first step?
A. It is a perfect square trinomial, so find the square root of the first and
last term.
B. It is a difference of squares so find the square roots for the first and last
term.
C. Find the greatest common factor (GCF).
D. The expression is prime it cannot be factored.

Answer 1

we conclude that the first step is to find the greatest common factor (GCF).

Hence, option C is correct.

Explanation:

`16x^2\:-36`

As 4 is the greatest common factor of the expression, so factor out common term 4:

i.e.

`16x^2\:-36=4\left(4x^2-9\right)`

Thus, the first step is to find the greatest common factor (GCF)

Now, solving the remaining portion

`16x^2\:-36=4\left(4x^2-9\right)`

as (2x+3) and (2x-3) are the factors of (4x²-9)

i.e. (4x²-9) = (2x+3) (2x-3)

Thus, the expression becomes

`16x^2\:-36=4\left(2x+3\right)\left(2x-3\right)`

Therefore, we conclude that the first step is to find the greatest common factor (GCF).

Hence, option C is correct.