Question

question
factor completely.
$2x^2 - 15x + 7$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(2\times7 = 14\) and add up to \(- 15\). The numbers are \(-1\) and \(-14\) since \((-1)\times(-14)=14\) and \((-1)+(-14)=-15\).

Step2: Rewrite the middle term

Rewrite \(-15x\) as \(-x - 14x\) in the expression \(2x^{2}-15x + 7\):
\(2x^{2}-x-14x + 7\)

Step3: Group and factor

Group the first two terms and the last two terms:
\((2x^{2}-x)-(14x - 7)\)
Factor out the greatest common factor from each group:
\(x(2x - 1)+(-7)(2x - 1)\)

Step4: Factor out the common binomial

Factor out the common binomial \((2x - 1)\):
\((2x - 1)(x - 7)\)

Answer:

\((2x - 1)(x - 7)\)