Question

factor $2x^2 - 11x - 6$ showing all steps

Explanation:

Step1: Split middle term

Find two numbers that multiply to $2\times(-6)=-12$ and add to $-11$. These numbers are $-12$ and $1$. Rewrite the middle term:
$2x^2 - 12x + x - 6$

Step2: Group terms

Group the first two and last two terms:
$(2x^2 - 12x) + (x - 6)$

Step3: Factor out GCF from groups

Factor out $2x$ from first group, 1 from second:
$2x(x - 6) + 1(x - 6)$

Step4: Factor common binomial

Factor out $(x - 6)$ from both terms:
$(2x + 1)(x - 6)$

Answer:

$(2x + 1)(x - 6)$