Question

Find the value of $-k$ so that $(x-3)$ is a factor of $3x^2+11x+k$.

Answer 1

If $(x-3)$ is the factor of the given polynomial $f\left(x\right)=3x^2+11x+k$

then $f\left(3\right)=0$. (by factor theorem)

Now, substituting $x=3$ in the given polynomial, we have:

$f\left(3\right)=3(3{)}^2+(11\times 3)+k$

$\Rightarrow 0=(3\times 9)+33+k$

$\Rightarrow 0=27+33+k$

$\Rightarrow 0=60+k$

$\Rightarrow -k=60$

Hence, $k=-60$.