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

1 Answer
Aug 3, 2018

#" "#
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.