Question

factor the trinomial.
8m² - 22m - 21

8m² - 22m - 21 = \square

Explanation:

Step1: Use AC method for factoring

For trinomial \(ax^2 + bx + c\) (here \(a = 8\), \(b=-22\), \(c = - 21\)), first find \(ac=8\times(-21)=-168\). We need two numbers that multiply to \(-168\) and add to \(-22\). The numbers are \(-28\) and \(6\) (since \(-28\times6=-168\) and \(-28 + 6=-22\)).

Step2: Rewrite the middle term

Rewrite \(-22m\) as \(-28m+6m\):

$$ 8m^2-28m + 6m-21 $$

Step3: Group and factor

Group the first two and last two terms:

$$ (8m^2-28m)+(6m - 21) $$

Factor out the GCF from each group: \(4m(2m - 7)+3(2m - 7)\)

Step4: Factor out the common binomial

Factor out \((2m - 7)\):

$$ (4m + 3)(2m - 7) $$

Answer:

\((4m + 3)(2m - 7)\)