Question

6a^2 -54factor polynomial completely and state if it’s prime.

Answer 1

Let's factor the polynomial, first we factor the common factor 6

`6a^2-54=6(a^2-9)`

the term in parenthesis is a difference of square, this can be factor by the rule:

`x^2-y^2=(x+y)(x-y)`

Then we have:

`\begin{gathered} 6a^2-54=6(a^2-9) \\ =6(a+3)(a-3) \end{gathered}`

Therefore the factor polynomial is:

`6(a+3)(a-3)`