Find the product of the following polynomials and state the degree of their product.

$x^{3} - 1; x^{2} - x + 4$

x^{5} - x^{4} - 4 x^{3} - x^{2} + x - 4

, degree 5.

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x^{5} - x^{4} + 4 x^{3} - x^{2} - x - 4

, degree 5.

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x^{5} - x^{4} + 4 x^{3} - x^{2} + x - 4

, degree 5.

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x^{5} + x^{4} + 4 x^{3} - x^{2} + x - 4

, degree 5.

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Solution

The correct option is D $x^{5} - x^{4} + 4 x^{3} - x^{2} + x - 4$ , degree 5.
$(x^{3} - 1) (x^{2} - x + 4)$

$= x^{3} (x^{2} - x + 4) - 1 (x^{2} - x + 4)$
$= x^{5} - x^{4} + 4 x^{3} - x^{2} + x - 4$
$= x^{5} - x^{4} + 4 x^{3} - x^{2} + x - 4$
$∴$ Degree is $5$

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