Question

factor completely.
-3v^{2}-4v + 4

Explanation:

Step1: Multiply -1 to make leading - coefficient positive

$3v^{2}+4v - 4$

Step2: Use AC - method

For $ax^{2}+bx + c$ (here $a = 3$, $b = 4$, $c=-4$), find two numbers that multiply to $ac=3\times(-4)=-12$ and add up to $b = 4$. The numbers are 6 and - 2.

Step3: Rewrite the middle term

$3v^{2}+6v-2v - 4$

Step4: Group the terms

$(3v^{2}+6v)-(2v + 4)$

Step5: Factor out the greatest common factor from each group

$3v(v + 2)-2(v + 2)$

Step6: Factor out the common binomial factor

$(v + 2)(3v-2)$

Step7: Remember the - 1 we factored out in Step1

$-(v + 2)(3v - 2)$

Answer:

$-(v + 2)(3v - 2)$