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Factor x3 + 2x2 + x completely. (x + 1)2 x(x2 + 1) x(x + 1)2

User Maltie
by
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2 Answers

3 votes

Answer:

x(x+1)^2

Explanation:

User Nic Benders
by
7.5k points
1 vote

Answer:


x(x+1)^2

Explanation:

Given:

The expression to factor is given as:


x^3+2x^2+x

In order to factor it, we write the factors of each of the terms of the given polynomial. So,

The factors of the three terms are:


x^3=x* x* x\\\\2x^2=2* x* x\\\\x=x

Now, 'x' is a common factor for all the three terms. So, we factor it out. This gives,


x((x^3)/(x)+2(x^2)/(x)+(x)/(x))\\\\x(x^2+2x+1)

Now, we know a identity which is given as:


(a+b)^2=a^2+2ab+b^2

Here,
x^2+2x+1 can be rewritten as
x^2+2(1)(x)+1^2

So,
a=x\ and\ b=1

Thus,
x^2+2(1)(x)+1^2= (x+1)^2

Therefore, the complete factorization of the given expression is:


x^3+2x^2+x=x(x+1)^2

User FredericK
by
8.5k points

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