Question

Check in which case the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial:
$t^2-3, 2t^4+3t^3-2t^2-9t-12$

Answer 1

$t^2-3,2t^4+3l:t^3-2t^2-9t-12$Fist polynomial is $t^2$

Second Polynomial is

$2^4+3t^{3}2t^{2}9t-12$Let us divide

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

$t^2-3)2t^4+3t^3-2t^2-9t-12(2t^2+3t+42t^4+0-6t^2$- + - ..........

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

$3t^3+0-9t$- + -

...............

$4t^2+0-12$

$4t^2+0-12$............

0The remainder is zero , therefore $t^2-3$ is a factor of $2t^4+3t^3-2t^2-9t-12$