Check whether the first polynomial is a factor of the second polynomial by dividing second polynomial by the first polynomial.
$x^{2} + 3 x + 1, 3 x^{4} + 5 x^{3} - 7 x^{2} + 2 x + 2$

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Solution

$x^{2} + 3 x + 1$ is a factor of $3 x^{4} + 5 x^{3} - 7 x^{2} + 2 x + 2$
Quotient of the division is $3 x^{2} - 4 x + 2$

Since, the remainder is zero, so $x^{2} + 3 x + 1$ is factor of $3 x^{4} + 5 x^{3} - 7 x^{2} + 2 x + 2$ .
Thus, $\frac{3 x^{4} + 5 x^{3} - 7 x^{2} + 2 x + 2}{x^{2} + 3 x + 1} = 3 x^{2} - 4 x + 2$

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

Question 2 (ii)
Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial:

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

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

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