# How do you find the degree of P(x) = x(x-3)(x+2) ?

Aug 3, 2018

$\text{ }$
The degree of the polynomial color(red)(P(x)=x(x-3)(x+2) is color(blue)(3

#### Explanation:

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Given:

color(red)(P(x)=x(x-3)(x+2)

color(green)("Step 1"

Multiply the factors to simplify:

Multiply $x \left(x - 3\right)$

$\Rightarrow \left({x}^{2} - 3 x\right)$

Next,

multiply $\left({x}^{2} - 3 x\right) \left(x + 2\right)$

$\Rightarrow x \left({x}^{2} - 3 x\right) + 2 \left({x}^{2} - 3 x\right)$

$\Rightarrow {x}^{3} - 3 {x}^{2} + 2 {x}^{2} - 6 x$

$\Rightarrow {x}^{3} - {x}^{2} - 6 x$

color(green)("Step 2"

$P \left(x\right) = {x}^{3} - {x}^{2} - 6 x$

All the terms are organized with the largest exponent first.

This is a polynomial with the largest exponent color(red)(3.

This is a cubic function.

color(green)("Step 3"

Degree of a polynomial refers to the

color(red)("largest exponent of the input variable" used.

The terms Degree and Order are used interchangeably.

Hence,

the degree of the polynomial color(blue)(P(x)=x(x-3)(x+2) is color(red)(3.

Hope it helps.