Question

factor completely.
$5f^{2}-16f + 3$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(5\times3 = 15\) and add up to \(- 16\). The numbers are \(-15\) and \(-1\) since \((-15)\times(-1)=15\) and \(-15 + (-1)=-16\).

Step2: Split the middle term

Rewrite the middle term \(-16f\) using \(-15f\) and \(-f\):
\(5f^{2}-15f - f + 3\)

Step3: Group and factor

Group the first two terms and the last two terms:
\((5f^{2}-15f)+(-f + 3)\)
Factor out the greatest common factor from each group:
\(5f(f - 3)-1(f - 3)\)

Step4: Factor out the common binomial

Factor out \((f - 3)\):
\((5f - 1)(f - 3)\)

Answer:

\((5f - 1)(f - 3)\)