Question

mpletely.
$4x^2 - 12x + 5$
attempt 2 out of 2

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(4\times5 = 20\) 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 quadratic expression:
\(4x^{2}-10x - 2x + 5\)

Step3: Group and factor

Group the first two terms and the last two terms:
\((4x^{2}-10x)+(-2x + 5)\)
Factor out the greatest common factor from each group:
\(2x(2x - 5)-1(2x - 5)\)

Step4: Factor out the common binomial

Now, factor out the common binomial \((2x - 5)\):
\((2x - 5)(2x - 1)\)

Answer:

\((2x - 5)(2x - 1)\)