poveli1e

2022-01-29

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

bemolizisqt

Expert

Explanation:
Given:
P(x)=x(x-3)(x+2)
Step 1
Multiply the factors to simplify:
Multiply x(x-3)
$⇒\left({x}^{2}-3x\right)$
Next,
multiply $\left({x}^{2}-3x\right)\left(x+2\right)$
$⇒x\left({x}^{2}-3x\right)+2\left({x}^{2}-3x\right)$
$⇒{x}^{3}-3{x}^{2}+2{x}^{2}-6x$
$⇒{x}^{3}-{x}^{2}-6x$
Step 2
$P\left(x\right)={x}^{3}-{x}^{2}-6x$
All the terms are organized with the largest exponent first.
This is a polynomial with the largest exponent 3.
This is a cubic function.
Step 3
Degree of a polynomial refers to the
largest exponent of the input variable used.
The terms Degree and Order are used interchangeably.
Hence,
the degree of the polynomial P(x)=x(x-3)(x+2) is 3.

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