Question

Multiply the following polynomials, find the degree of the product polynomial:

$p (x) = x^{2} + 3 x + 2; q (x) = x^{2} + 3 x + 1$

Accepted Answer

Given,

$p (x) = x^{2} + 3 x + 2; q (x) = x^{2} + 3 x + 1$

To multiply two polynomials first multiply all the terms of first polynomial with all the terms of second polynomial then collect similar terms and then add/subtract its coefficients.

So, $p (x) \times q (x) = (x^{2} + 3 x + 2) (x^{2} + 3 x + 1)$

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

$= x^{4} + 3 x^{3} + x^{2} + 3 x^{3} + 9 x^{2} + 3 x + 2 x^{2} + 6 x + 2$

$= x^{4} + 3 x^{3} + 3 x^{3} + 9 x^{2} + x^{2} + 2 x^{2} + 3 x + 6 x + 2$

$= x^{4} + 6 x^{3} + 12 x^{2} + 9 x + 2$

Hence, the required product polynomial is $x^{4} + 6 x^{3} + 12 x^{2} + 9 x + 2$ .

Now, the degree of a polynomial is the highest of the degrees of the polynomial's with non-zero coefficients.

So, the degree of the product polynomial $x^{4} + 6 x^{3} + 12 x^{2} + 9 x + 2$ is $4$ .

Chhattisgarh Board Solutions for Exercise 12: Try This

Chhattisgarh Board Mathematics Solutions for Exercise - Chhattisgarh Board Solutions for Exercise 12: Try This

Questions from Chhattisgarh Board Solutions for Exercise 12: Try This with Hints & Solutions

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