Check whether x3 -3x + 1 , is the factor of x5-4x3+x2+3x +1.
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Check whether x3 -3x + 1 , is the factor of x5-4x3+x2+3x +1.
answer with full explanation and ans only of you can no spamming
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Answer:
[tex](x^{3} -3x+1)[/tex] is not a factor of [tex](x^{5} -4x^{3} + x^{2} + 3x + 1)[/tex]
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 [tex]p(x) = x^{3} -3x+1[/tex] is a factor of [tex]f(x) = x^{5} - 4x^{3} + x^{2} + 3x + 1[/tex]
⇒ [tex]\frac{f(x)}{p(x)}[/tex]
Check the attachment for complete steps of division
After long division;
We get a Remainder[tex](R) = 2[/tex] and Quotient[tex](Q) = x^{2} -1[/tex]
Since, we get a remainder it means that [tex]p(x)= x^{3} - 3x + 1[/tex] is not a factor of [tex]f(x) = x^{5} -4x^{3} + x^{2} + 3x + 1[/tex]