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

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

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Answer 1 · 2018-08-03T01:44:08

$" "$
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.

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

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