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

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

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Answer 1 · 2018-08-03T01:44:08

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

Explanation:

$" "$
Given:

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

$Step 1$ $color(green)("Step 1"$

Multiply the factors to simplify:

Multiply $x (x - 3)$ $x(x-3)$

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

Next,

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

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

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

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

$Step 2$ $color(green)("Step 2"$

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

All the terms are organized with the largest exponent first.

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

This is a cubic function.

$Step 3$ $color(green)("Step 3"$

Degree of a polynomial refers to the

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

The terms Degree and Order are used interchangeably.

Hence,

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

Hope it helps.

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

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

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