Question

Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial.

$t^2-3,2t^4+3t^3-2t^2-9t-12$

• A. Yes, $t^2-3$ is a factor.
• B. No, $t^2-3$ is not a factor.
• C. Ambiguous
• D. Data insufficient

Answer 1

The correct option is A Yes, $t^2-3$ is a factor.

Let's use division method,

$t^2-3\left)\overline{2t^4+3t^3-2t^2-9t-12}\right(2t^2+3t+4$
$\underset{–}{\underset{-}{2t^4}\underset{+}{-6t^2}}$
$3t^3+4t^2-9t-12$
$\underset{–}{\underset{-}{3t^3}\underset{+}{-9t}}$
$4t^2-12$
$\underset{–}{\underset{-}{4t^2}-\underset{+}{12}}$
$0$

Since on dividing $2t^4+3t^3-2t^2-9t-12$ by $t^2-3$. We get the remainder 0.

Hence, $t^2-3$ is a factor of $2t^4+3t^3-2t^2-9t-12$.