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Multiplication of Any Polynomial

If p x = x ...

Question

If $p (x) = x^{2} - 2 x + 1$ and $q (x) = x^{3} - 3 x^{2} + 2 x - 1$ . Find $p (x) \times q (x)$ and check the degree of $p (x) \times q (x)$ .

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Solution

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

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

$= (x^{5} - 3 x^{4} + 2 x^{3} - x^{2}) + (- 2 x^{4} + 6 x^{3} - 4 x^{2} + 2 x) + (x^{3} - 3 x^{2} + 2 x - 1)$

$= x^{5} - x^{4} + 9 x^{3} - 8 x^{2} + 4 x - 1$
And the degree is 5 of $x^{5}$

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