Question

If $(x-3)$ is the factor of $3x^3-x^2+px+q$, then ..................

• A. $p+q=72$
• B. $3p+q=72$
• C. $3p+q=-72$
• D. $q-3p=72$

Answer 1

The correct option is C $3p+q=-72$

Since $x-3$ is a factor of $f\left(x\right)=0$, so $f\left(3\right)=0$
$\therefore$ $3\times (3{)}^3-(3{)}^2+p\times 3+q=0$
$\therefore$ $81$ - $9+3p+q=0$
$\therefore$ $3p+q=-72$