Question

factor.
$2x^2 - 7x + 5$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(2\times5 = 10\) and add up to \(-7\). The numbers are \(-2\) and \(-5\) since \((-2)\times(-5)=10\) and \(-2 + (-5)=-7\).

Step2: Rewrite the middle term

Rewrite \(-7x\) as \(-2x - 5x\) in the quadratic expression:
\(2x^{2}-2x - 5x + 5\)

Step3: Group and factor

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

Step4: Factor out the common binomial

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

Answer:

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