Question

question
factor completely.
$2x^2 - 7x - 4$

Explanation:

Step1: Find two numbers for factoring

We need two numbers that multiply to \(2\times(-4) = -8\) and add up to \(-7\). The numbers are \(-8\) and \(1\) since \(-8\times1=-8\) and \(-8 + 1=-7\).

Step2: Rewrite the middle term

Rewrite \(-7x\) as \(-8x+x\) in the expression \(2x^{2}-7x - 4\):
\(2x^{2}-8x+x - 4\)

Step3: Group and factor

Group the first two terms and the last two terms:
\((2x^{2}-8x)+(x - 4)\)
Factor out the greatest common factor from each group:
\(2x(x - 4)+1(x - 4)\)

Step4: Factor out the common binomial

Factor out the common binomial \((x - 4)\):
\((2x + 1)(x - 4)\)

Answer:

\((2x + 1)(x - 4)\)