# Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial:$x^3 -3x + 1, x^5 - 4x^3 + x^2 + 3x + l$

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Given:

$x^3\ –\ 3x\ +\ 1$ and $x^5\ –\ 4x^3\ +\ x^2\ +\ 3x\ +\ 1$.

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$f(x)\ =\ x^5\ –\ 4x^3\ +\ x^2\ +\ 3x\ +\ 1$

Divisor$g(x)\ =\ x^3\ –\ 3x\ +\ 1$

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

$x^3-3x+1$)$x^5-4x^3+x^2+3x+1$($x^2-1$

$x^5-3x^3+x^2$

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$-x^3+3x+1$

$-x^3+3x-1$

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$0$

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

Updated on 10-Oct-2022 13:19:38