The factor of the expression x 3 + 2 x 2 + x .

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 1.3, Problem 115E
To determine

To calculate: The factor of the expression x3+2x2+x .

Expert Solution

The factor of the expression x3+2x2+x is x(x+1)2 .

Explanation of Solution

Given information:

The expression x3+2x2+x .

Formula used:

The special factoring formula of perfect square which is expressed as,

X2+2XY+Y2=(X+Y)2

Calculation:

Consider the given expression x3+2x2+x .

Rewrite it as,

x3+2x2+x=x(x2+2x+1)=x[(x)2+2(x)(1)+(1)2]

Recall the special factoring formula of perfect square which is expressed as,

X2+2XY+Y2=(X+Y)2

Here, the values of X and Y are X=x and Y=1 .

x3+2x2+x=x[(x)2+2(x)(1)+(1)2]=x(x+1)2

Thus, the factor of expression x3+2x2+x is x(x+1)2 .

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