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Combination

Find the prod...

Question

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

$3 x^{2} + 5 x; x^{2} + 2 x + 1$

3 x^{4} + 11 x^{3} + 13 x^{2} + 5 x

, degree 4.

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

, degree 3.

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x^{2} + x

, degree 2.

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0

, degree 0.

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Solution

The correct option is A $3 x^{4} + 11 x^{3} + 13 x^{2} + 5 x$ , degree 4.
$(3 x^{2} + 5 x) (x^{2} + 2 x + 1)$

$= 3 x^{2} (x^{2} + 2 x + 1) + 5 x (x^{2} + 2 x + 1)$

$= 3 x^{4} + 6 x^{3} + 3 x^{2} + 5 x^{3} + 10 x^{2} + 5 x$
$= 3 x^{4} + 11 x^{3} + 13 x^{2} + 5 x$
$∴$ Degree is $4$

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