Question

Check whether $7+3x$ is a factor of $3x^3+7x$. [2 MARKS]

Answer 1

Concept: 0.5 Mark
Application: 1 Mark
Calculation: 0.5 Mark

If $(x-a)$ is a factor of $p\left(x\right)$, then $p\left(a\right)=0$

Zero of $(7+3x)$ is $x=-\frac{7}{3}$

$p(-\frac{7}{3})=3{(-\frac{7}{3})}^3+7(-\frac{7}{3})$

$=-\frac{343}{9}-\frac{49}{3}$

$=-\frac{490}{9}\ne 0$

Hence, $(7+3x)$ is not a factor of $3x^3+7x$.