Question

$\text{If the remainder of}p\left(x\right)=3x+7\text{when divided by}x+8\text{is the zero of the}\text{polynomial}q\left(x\right)=2x-a,\text{then what is the}\text{value of}a?$

• A. 34
• B. -17
• C. -34
• D. 17

Answer 1

The correct option is C -34

$\text{By remainder theorem, we know that}\text{if a polynomial f(x) is divided by}\text{(x - a), the remainder obtained is f(a).}$

$\text{From remainder theorem, when}p\left(x\right)\text{is divided with}x+8,\text{the remainder is}p(-8).$
$\therefore x+8=0x=(-8)$

$\therefore p(-8)=-3\left(8\right)+7=-17$

$\text{Given -17 is a zero of}q\left(x\right)=2x-a$
$\Rightarrow$ $q(-17)=0$
$\Rightarrow$ $2(-17)-a=0$
$\Rightarrow$ $a=-34$