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Expert: - 11/7/2008


Question
we are learning to factor quadratic equations in my online college algebra class and I'm so LOST!  not even sure where to begin with this problem:  5x^2y^6z^4 - 15x^4y^5z^3 + 20x^3y^5z^2.  could you please help me??

Answer
Note which terms are the same in each factor.  I will look at each of the terms in order on each of the problems.

As far as the constants go, we have 5, -15, and 20, which are all divisible by 5.

Now lets look at the powers of x.  They are 2, 4, and 3, so we can factor out an x².

Lets look at the powers of y.  They are 6, 5, and 5, so we can factor out a y^5.

Finally, lets look at the powers of z.  They are 4, 3, and 2, so we can factor out z².

Putting all of these together, it looks like we can factor out
5x²y^5z² from each of the terms.  To do so, write them down and look at the constant, the power on x, the power on y, and then the power on z.

The first term is left with 5x^2y^6z^4/(5x²y^5z²) = yz².
The second term is left with -15x^4y^5z^3/(5x²y^5z²) = -3x²z.
The third term is left with 20x^3y^5z^2/(5x²y^5z²) = 4x.

This gives us (5x²y^5z²)(yz² - 3x²z + 4x).

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