Question

which of the binomials below is a factor of this trinomial? 5x^2 - 5x - 100A. x + 10B. x - 5C. x + 5D. x - 4

Answer 1

B

1) As we can see all coefficients are divisible by 5. That leads us to opt to factor out the common factor technique.

`\begin{gathered} 5x^2-5x-100 \\ \\ 5\left(x^2-x-20\right) \\ \\ \end{gathered}`

2) Now, let's focus on factoring the trinomial inside the parentheses. Note that we need to find two numbers whose sum is -1 and simultaneously their product is -20.

By guess and check, we know these numbers are -5 and 4.

`\begin{gathered} -5+4=-1 \\ -5*4=-20 \end{gathered}`

`\begin{gathered} 5\lbrack\lparen x-5)(x+4)\rbrack \\ \\ 5(x-5)(x+4) \end{gathered}`

Thus, the answer is B