How to factor polynomials: Difference between revisions

Revision as of 20:52, 6 October 2009

Revision as of 21:00, 6 October 2009

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:<math>y^2-9=(y+3)(y-3),\,\!</math><br />

or<br />

:<math>16a^2-49b^2=(4a+7b)(4a-7b),.\,\!</math>

<br /><br />

'''Sum of Cubes:'''<br />

:<math>x^3+y^3=(x+y)(x^2-xy+y^2),\,\!</math><br />

For example:

:<math>z^3+27=(z+3)(z^2-3z+9),\,\!</math><br />

or<br />

:<math>8x^3+125=(2x)^3+(5)^3=(2x+5)[(2x)^2-(5)(2x)+(5)^2]=(2x+5)(4x^2-10x+5).\,\!</math>

<br /><br />

'''Difference of Cubes:'''<br />

:<math>x^3-y^3=(x-y)(x^2+xy+y^2),\,\!</math><br />

For example:

:<math>z^3-27=(z-3)(z^2+3z+9),\,\!</math><br />

or<br />

:<math>8x^3-125=(2x)^3+-(5)^3=(2x-5)[(2x)^2+(5)(2x)+(5)^2]=(2x-5)(4x^2+10x+5).\,\!</math>

==References==