Check whether the first polynomial is a factor of the second polynomial by applying the division algorithm:
$g(t)\ =\ t^2\ –\ 3;\ f(t)\ =\ 2t^4\ +\ 3t^3\ –\ 2t^2\ –\ 9t\ –\ 12$

Given:

$g(t)\ =\ t^2\ –\ 3$ and $f(t)\ =\ 2t^4\ +\ 3t^3\ –\ 2t^2\ –\ 9t\ –\ 12$.

To do:

We have to check whether $g(t)$ is a factor of $f(t)$ by applying the division algorithm.

Solution:

On applying the division algorithm, 

Dividend$f(t)\ =\ 2t^4\ +\ 3t^3\ –\ 2t^2\ –\ 9t\ –\ 12$

Divisor$g(t)\ =\ t^2\ –\ 3$

If $g(t)$ is a factor of $f(t)$ then the remainder on long division should be $0$.

$t^2-3$)$2t^4+3t^3-2t^2-9t-12$($2t^2+3t+4$

                $2t^4          -6t^2$

               -------------------------------

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

$3t^3 -9t$

--------------------------------

$4t^2-12$

$4t^2-12$

----------------

$0$

Therefore, $g(t)$ is a factor of $f(t)$.

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Updated on: 10-Oct-2022

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