Question

Verify whether 5 + 2x a factor of $2x^3+5x+\frac{175}{4}$ ? [3 MARKS]

Answer 1

Concept : 1 Mark
Application : 1 Mark
Calculation : 1 Mark

We know that,

$(x-a)$ is a factor of $f\left(x\right)$ if $f\left(a\right)=0$

$5+2x=0\Rightarrow x=-\frac{5}{2}$

$f\left(x\right)=2x^3+5x+\frac{175}{4}$

$f(-\frac{5}{2})=2(-\frac{5}{2}{)}^3+5(-\frac{5}{2})+\frac{175}{4}$

$\Rightarrow f(-\frac{5}{2})=0$

$\therefore 5+2x$ is a factor of $2x^3+5x+\frac{175}{4}$