Question

$\text{Using factor theorem find which of the}\text{following is a factor of the polynomial}p\left(x\right)=3x^2+10x+7.$

• A. $(x+1)$
• B. $(x+7)$
• C. $(x-1)$
• D. $(x-7)$

Answer 1

The correct option is A $(x+1)$

Given polynomial: $p\left(x\right)=3x^2+10x+7$

$\text{By factor theorem, if}(x-a)\text{is a factor}\text{of}p\left(x\right),\text{then}p\left(a\right)=0$

$\text{Checking}(x+1):$
$p(-1)=3\times (-1{)}^2+10\times (-1)+7$
$p(-1)=0$
$\text{Hence,}(x+1)\text{is a factor of}p\left(x\right).$

$\text{Checking}(x+7):$
$p(-7)=3\times (-7{)}^2+10\times (-7)+7$
$p(-7)=147-70+7=84\ne 0$
$\text{Hence,}(x+7)\text{is not a factor of}p\left(x\right).$

$\text{Checking}(x-1):$
$p\left(1\right)=3\times (1{)}^2+10\times (1)+7$
$p\left(1\right)=20$
$\text{Hence,}(x-1)\text{is a not factor of}p\left(x\right).$

$\text{Checking}(x-7):$
$p\left(7\right)=3\times (7{)}^2+10\times (7)+7$
$p\left(7\right)=147+70+7=224\ne 0$
$\text{Hence,}(x-7)\text{is not a factor of}p\left(x\right).$

$\text{So,}(x+1)\text{is the factor of the}\text{polynomial}p\left(x\right)=3x^2+10x+7.$