Try our Free Online Math Solver!

Factoring Polynomials
The process of factoring a polynomial is analogous to the
process of factoring
an integer into its prime factors. For example 180 factors as 2^{2}3^{2}5. We want
to do the same thing, but with polynomials.
Factoring out the Greatest Common Factor
Example.
Factoring by Grouping
Method : Group terms in pairs depending on whether they have common
factors, then factor out common term .
Example.
Example. −10z + 6yz + 5 − 3y
Factoring polynomials of the form ax^{2} + bx + c
Polynomials of this form (degree 2) are called quadratic polynomials .
Method : Find two numbers whose sum is b and whose product is ac. Replace
b by the sum of these two numbers, and factor the resulting polynomial by
grouping .
Example. 12b^{2} + 17b + 6
Example. x^{2 }− 4x − 12
Factoring Special Products
1) Difference of Two Squares a ^{2} − b^{2} = (a + b)(a − b)
2) Perfect Square Trinomial a^{2} + 2ab + b^{2} = (a + b)^{2
}
3) Perfect Square Trinomial a ^{2} − 2ab + b^{2} = (a − b)^{2
}
4) Difference of Two Cubes a^{3}−b^{3} = (a−b)(a^{2}+ab+b^{2})
5) Sum of Two Cubes a ^{3}+b^{3} = (a+b)(a^{2}−ab+b^{2})
Example. 9t^{2} − v^{2
}
Example. 4w^{2} − 4w + 1
Example. 9x^{2} − 12xy + 4y^{2
}
Example. m^{3} + n^{3
}
Example. a^{3} − 8
Example. 8t^{3}h^{3} + n^{9}
Factoring Completely
Example. a^{4}b^{2} − 16b^{2}
Example. a^{3} + a^{2} − 4a − 4
Example. −36x^{3} + 18x^{2} + 4x
Example. a^{7} − a^{6} − 64a + 64
Prev  Next 