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Factoring Methods

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Factoring out the Greatest Common Factor

Factoring out the greatest common factor (GCF) is always a good idea. This can simplify the equation into something more workable. A great first step in any factoring equation, and that is why it is on the first page of the factoring examples.

Example 1:

If we start with the polynomial equation

12 x^{4} y + 15 x^{3} y^{2} - 21 x^{2} y^{4}

, we would first look for the greatest common factors that can be taken out of the equation. The numbers at the beginning of each section of the equation are all divisible by 3 so that would be our first step. The equation would then look like

3 ({4x}^{4} y + 5 x^{3} y^{2} - 7 x^{2} y^{4})

. The next step in reducing to the greatest common factor is taking out x’s and y’s. In this equation we can take out

x^{2}

and y. Then the equation would look like

3 x^{2} y ({4x}^{2} + 5 x y - 7 y^{3})

. (Factor Out The Greatest Common Factor (GCF))

Example 2:

I will give one more example of removing the greatest common factor with the problem shown here:

18 x^{4} y^{5} + 36 x^{3} y^{7}

. When we look at this equation, it should become apparent that 18 can be taken out, and

x^{3}

and

y^{5}

. The end result of taking out these factors is

18 x^{3} y^{5} (x + 2 y^{2})

. (Factor Out The Greatest Common Factor (GCF))