Question

completely.
$4x^2 + 7x - 2$
swer attempt 1 out of 2

Explanation:

Step1: Find two numbers

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

Step2: Rewrite the middle term

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

Step3: Group and factor

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

Step4: Factor out the common binomial

Factor out \((x + 2)\) from both terms: \((4x - 1)(x + 2)\).

Answer:

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