Find the product of the following polynomials and state the degree of their product.
$x^{2} + 3 x + 1; 2 x - 3$

2 x^{3} + 3 x^{2} - 7 x - 3

, degree 3.

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x^{2} - 7 x - 3

, degree 2.

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3

, degree 0.

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x - 3

, degree 1.

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Solution

The correct option is C $2 x^{3} + 3 x^{2} - 7 x - 3$ , degree 3.
$(x^{2} + 3 x + 1) (2 x - 3)$

$= x^{2} (2 x - 3) + 3 x (2 x - 3) + (2 x - 3)$
$= 2 x^{3} - 3 x^{2} + 6 x^{2} - 9 x + 2 x - 3$
$= 2 x^{3} + 3 x^{2} - 7 x - 3$
$∴$ Degree is $3$

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