Factoring x^5+2x^4+x^3

Guest · Jul 12, 2006

Hi can anyone please help me with this problem?

x^5+2x^4+x^3

I only got as far as factoring the greatest monomial, x^3(x^2+2x).

I'm not sure what to do next. I looked in the back of the book and the answer is x^3(x+1)^2

Please help me!

jonboy · Jul 12, 2006

Hello 071206!

071206 said:
Hi can anyone please help me with this problem?

x^5+2x^4+x^3

I only got as far as factoring the greatest monomial, x^3(x^2+2x).

I'm not sure what to do next. I looked in the back of the book and the answer is x^3(x+1)^2

Please help me!

Good job so far. But you need a 1 in their for the \(\displaystyle \L x^3\)

We have \(\displaystyle \L x^5+2x^4+x^3\)

Use the greatest monomial \(\displaystyle \L x^3(x^2+2x+1)\)

Now we must factor \(\displaystyle \L x^2+2x+1\). What two numbers multiply to give you \(\displaystyle \L 1\) and add up to \(\displaystyle \L 2\)? Those would be \(\displaystyle \L 1 & 1\)

So the factor for that is \(\displaystyle \L (x+1)(x+1)\)

So your answer is \(\displaystyle \L x^3(x+1)(x+1)\to x^3(x+1)^2\)

Mrspi · Jul 13, 2006

071206 said:
Hi can anyone please help me with this problem?

x^5+2x^4+x^3

I only got as far as factoring the greatest monomial, x^3(x^2+2x).

I'm not sure what to do next. I looked in the back of the book and the answer is x^3(x+1)^2

Please help me!

You correctly noted that each term has a factor of x3. But, to help you see how the "1" comes into play, let's rewrite the original expression to show what that x3 is multiplied by in each term:

x3 * x2 + x3 * 2x + x3*1

Now, put the common factor of x3 OUTSIDE a set of parentheses, and what is left from each term INSIDE the parentheses:

x3(x2 + 2x + 1)

If you try multiplying back your attempt at removing the common factor, you'll find that you do NOT get the expression you started with!

Next, factor the expression inside the parentheses.....it is the square of a binomial.

Factoring x^5+2x^4+x^3

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jonboy

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Mrspi

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