What is the degree of polynomial $P$ defined by :
$P (x) = 2 (x - 2) (x^{2} + 5)$ ?

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Solution

Solve the polynomial as follows:

$2 (x - 2) (x^{2} + 5)$
$= (2 x - 4) (x^{+} 5)$
$= 2 x^{3} + 10 x - 4 x^{2} - 20$ or
$= 2 x^{3} - 4 x^{2} + 10 x - 20$

Since the highest exponent of its term is the degree of a polynomial and here the highest exponent is 3.

Hence the degree of the given polynomial is 3.

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