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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:

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

Given:

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

To do:

We have to check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial.

Solution:

On applying the division algorithm,

Let dividend $f(x)=3x^4+5x^3-7x^2+2x + 2$

Divisor $g(x) =x^2 + 3x + 1

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

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

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