Question

factor
3v² - 4v - 7
(3v+1)(v-9)
(3v-7)(v+1)
3(v-7)(v-1)
(3v+1)(v-10)

Explanation:

Step1: Split middle term

Find two numbers that multiply to $3\times(-7)=-21$ and add to $-4$. The numbers are $3$ and $-7$. Rewrite the middle term:
$3v^2 + 3v - 7v - 7$

Step2: Factor by grouping

Group the first two and last two terms, then factor out common terms:
$3v(v+1) -7(v+1)$

Step3: Factor out common binomial

Extract the shared $(v+1)$ factor:
$(3v-7)(v+1)$

Step4: Verify options

Compare the result to the given choices.

Answer:

B. $(3v-7)(v+1)$