Question

question
factor completely.
$6x^2 - 17x - 3$
answer attempt 1 out of 2

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(6\times(-3)= -18\) and add up to \(-17\). The numbers are \(-18\) and \(1\) since \(-18\times1 = -18\) and \(-18 + 1=-17\).

Step2: Rewrite the middle term

Rewrite \(-17x\) as \(-18x+x\) in the expression \(6x^{2}-17x - 3\):
\(6x^{2}-18x+x - 3\)

Step3: Group and factor

Group the first two terms and the last two terms:
\((6x^{2}-18x)+(x - 3)\)
Factor out the greatest common factor from each group:
\(6x(x - 3)+1(x - 3)\)

Step4: Factor out the common binomial

Factor out \((x - 3)\) from both terms:
\((6x + 1)(x - 3)\)

Answer:

\((6x + 1)(x - 3)\)