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 \(-23x\) as \(-21x - 2x\) in the expression \(7x^{2}-23x + 6\):
\(7x^{2}-21x-2x + 6\)

Step3: Group the terms

Group the first two terms and the last two terms:
\((7x^{2}-21x)+(-2x + 6)\)

Step4: Factor out the GCF from each group

Factor out \(7x\) from the first group and \(-2\) from the second group:
\(7x(x - 3)-2(x - 3)\)

Step5: Factor out the common binomial factor

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

Answer:

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