Question

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

${\mathrm{t}}^2-3$, $2{\mathrm{t}}^4+3{\mathrm{t}}^3-2{\mathrm{t}}^2-9\mathrm{t}-12$

Answer 1

Remainder Theorem:

Divisor $={\mathrm{t}}^2-3$

Dividend $=2{\mathrm{t}}^4+3{\mathrm{t}}^3-2{\mathrm{t}}^2-9\mathrm{t}-12$

We observe that, the remainder is left as $0$.

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