Question

Is p(x) a multiple of g(x) ?

$p\left(x\right)=2x^3-11x^2-4x+5,g\left(x\right)=2x+1$

• A. Yes
• B. No
• C. Cannot be determined
• D. Data Inadequate

Answer 1

Answer: (B)

No

Given, $p\left(x\right)=2x^3-11x^2-4x+5$
$g\left(x\right)=2x+1$
$=>2x+1=0$
$=>x=-\frac{1}{2}$
Now, $p(-\frac{1}{2})$ should be $0$ if $p\left(x\right)$ is a multiple of $g\left(x\right)$
Thus,
$p(-\frac{1}{2})=2(-\frac{1}{2}{)}^3-11(-\frac{1}{2}{)}^2-4(-\frac{1}{2})+5$
$=(-\frac{1}{4})+\left(\frac{11}{4}\right)+2+5$
$=\frac{10}{4}+2+5$
$\ne 0$
Thus, $p\left(x\right)$ is not a multiple of $g\left(x\right)$