Question

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

Answer 1

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

Explanation:

`" "`
Given:

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

`color(green)("Step 1"`

Multiply the factors to simplify:

Multiply `x(x-3)`

`rArr (x^2-3x)`

Next,

multiply `(x^2-3x) (x+2)`

`rArr x(x^2-3x)+2(x^2-3x)`

`rArr x^3-3x^2+2x^2-6x`

`rArr x^3-x^2-6x`

`color(green)("Step 2"`

`P(x)=x^3-x^2-6x`

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.