Question

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

Explanation:

Step1: Expand each option

For option \((3v - 7)(v + 1)\):
Using the distributive property \((a + b)(c + d)=ac+ad+bc+bd\), we have \(3v\times v+3v\times1-7\times v - 7\times1=3v^{2}+3v-7v - 7=3v^{2}-4v - 7\)

For option \((3v + 1)(v - 9)\):
\(3v\times v+3v\times(- 9)+1\times v+1\times(-9)=3v^{2}-27v + v-9=3v^{2}-26v - 9\)

For option \(3(v - 7)(v - 1)\):
First expand \((v - 7)(v - 1)=v^{2}-v-7v + 7=v^{2}-8v + 7\), then multiply by 3: \(3v^{2}-24v + 21\)

For option \((3v + 1)(v - 10)\):
\(3v\times v+3v\times(-10)+1\times v+1\times(-10)=3v^{2}-30v + v-10=3v^{2}-29v - 10\)

Step2: Compare with the original expression

The original expression is \(3v^{2}-4v - 7\), and the expansion of \((3v - 7)(v + 1)\) matches the original expression.

Answer:

A. \((3v - 7)(v + 1)\)