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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