Question

What should be subtracted from $x^3-7x^2+17x+17$ so that the difference is a multiple of $x-3$?

• A. $5$
• B. $32$
• C. $7$
• D. $43$

Answer 1

Answer: (B)

$32$

Polynomial $=x^3-7x^2+17x+17$

for the polynomial to be a multiple of $(x-3)$ it should be equal to zero for $x=3$. Let us substitute $x=3$ in the polynomial

${\left(3\right)}^3-7{\left(3\right)}^2+17\left(3\right)+17=27-63+51+17=32$

We know, that $p\left(x\right)=g\left(x\right)q\left(x\right)+r\left(x\right)$

if we subtract remainder from $p\left(x\right)$, we will get $p\left(x\right)$ as a multiple of $g\left(x\right)$

$\therefore$ 32 should be subtracted from polynomial.