Question

factor.
$7x^2 - 23x + 6$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(7\times6 = 42\) and add up to \(- 23\). The numbers are \(-21\) and \(-2\) since \((-21)\times(-2)=42\) and \(-21+( - 2)=-23\).

Step2: Rewrite the middle term

Rewrite the quadratic \(7x^{2}-23x + 6\) as \(7x^{2}-21x-2x + 6\).

Step3: Group and factor

Group the first two terms and the last two terms: \((7x^{2}-21x)+(-2x + 6)\).
Factor out the greatest common factor from each group: \(7x(x - 3)-2(x - 3)\).

Step4: Factor out the common binomial

Factor out \((x - 3)\) from both terms: \((7x-2)(x - 3)\).

Answer:

\((7x - 2)(x - 3)\)