Check whether the first polynomial is a factor of the second polynomial

Question.

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

(i) $t^{2}-3,2 t^{4}+3 t^{3}-2 t^{2}-9 t-12$

(ii) $x^{2}+3 x+1,3 x^{4}+5 x^{3}-7 x^{2}+2 x+2$

(iii) $x^{3}-3 x+1, x^{5}-4 x^{3}+x^{2}+3 x+1$


Solution:

Check whether the first polynomial is

Hence, $t^{2}-3$ is a factor of

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

(ii) $x^{2}+3 x+1$

. Check whether the first polynomial

Hence, $x^{2}+3 x+1$ is a factor of

$3 x^{4}+5 x^{3}-7 x^{2}+2 x+2$

(iii) $x^{3}-3 x+1$

Check whether the first polynomial is a factor

Hence, $x^{2}-3 x+1$ is not a factor of

$x^{5}-4 x^{3}+x^{2}+3 x+1$

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