Question

Check whether x3 -3x + 1 , is the factor of x5-4x3+x2+3x +1.

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Answer 1

Answer:

$(x^{3} -3x+1)$ is not a factor of $(x^{5} -4x^{3} + x^{2} + 3x + 1)$

Step-by-step explanation:

We can check whether a polynomial is a factor of another polynomial (of greater degree) by dividing them. If there is no remainder, then the polynomial is a factor.

⇒ In our case

We have to check whether $p(x) = x^{3} -3x+1$ is a factor of $f(x) = x^{5} - 4x^{3} + x^{2} + 3x + 1$

⇒ $\frac{f(x)}{p(x)}$

Check the attachment for complete steps of division

After long division;

We get a Remainder$(R) = 2$ and Quotient$(Q) = x^{2} -1$

Since, we get a remainder it means that $p(x)= x^{3} - 3x + 1$ is not a factor of $f(x) = x^{5} -4x^{3} + x^{2} + 3x + 1$