Question

question
factor completely.
$5x^2 - 12x + 4$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(5\times4 = 20\) and add up to \(-12\). The numbers are \(-10\) and \(-2\) since \((-10)\times(-2)=20\) and \(-10 + (-2)=-12\).

Step2: Rewrite the middle term

Rewrite \(-12x\) as \(-10x - 2x\) in the expression:
\(5x^{2}-10x - 2x + 4\)

Step3: Group the terms

Group the first two terms and the last two terms:
\((5x^{2}-10x)+(-2x + 4)\)

Step4: Factor out the GCF from each group

Factor out \(5x\) from the first group and \(-2\) from the second group:
\(5x(x - 2)-2(x - 2)\)

Step5: Factor out the common binomial factor

Factor out \((x - 2)\) from the expression:
\((5x - 2)(x - 2)\)

Answer:

\((5x - 2)(x - 2)\)