Question

factor completely.
3f² - 10f + 8
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Explanation:

Step1: Find two numbers for factoring

We need two numbers that multiply to \(3\times8 = 24\) and add up to \(- 10\). The numbers are \(-6\) and \(-4\) since \((-6)\times(-4)=24\) and \(-6 + (-4)=-10\).

Step2: Rewrite the middle term

Rewrite \(-10f\) as \(-6f-4f\) in the quadratic expression:
\(3f^{2}-6f - 4f + 8\)

Step3: Group the terms

Group the first two terms and the last two terms:
\((3f^{2}-6f)+(-4f + 8)\)

Step4: Factor out the GCF from each group

Factor out \(3f\) from the first group and \(- 4\) from the second group:
\(3f(f - 2)-4(f - 2)\)

Step5: Factor out the common binomial factor

Factor out \((f - 2)\) from the expression:
\((3f - 4)(f - 2)\)

Answer:

\((3f - 4)(f - 2)\)