A Summary of Factoring Polynomials
Factoring The Difference of 2 Squares
Factoring Trinomials
Quadratic Expressions
Factoring Trinomials
The 7 Forms of Factoring
Factoring Trinomials
Finding The Greatest Common Factor (GCF)
Factoring Trinomials
Quadratic Expressions
Factoring simple expressions
Factoring Polynomials
Fractoring Polynomials
Other Math Resources
Factoring Polynomials
Finding the Greatest Common Factor (GCF)
Factoring Trinomials
Finding the Least Common Multiples
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Special Factorizations

Four special factorizations occur so often that they arelisted here for future reference.} }


x - y = (x+y)(x-y) Difference of two squares

x + 2xy + y= (x+y) Perfect square

x - y = (x-y)(x+ xy + y) Difference of two cubes

x + y = (x+y)(x- xy + y) Sum of two cubes

A polynomial that cannot be factored is called a primepolynomial.


Factor each of the following.

(a) 64p-49q=(8p)-(7q)= (8p+7q)(8p-7q)

(b) x + 36 is a prime polynomial.

(c) x + 12x +36 = (x +6)

(d) 9y-24yz + 16z= (3y-4z)

(e) y - 8 = (y-2)(y+ 2y + 4)

(f ) m +125 = m + 5 = (m+5)(m-5m + 25)

(g) 8k-27z = (2k)-(3z) = (2k -3z)(4k+6kz +9z)


In factoring, always look for a common factor first. Since 36x- 4y has a common factor of 4,

36x - 4y = 4(9x- y) = 4(3x + y)(3x - y)

It would be incomplete to factor it as

36x - 4y = (6x + 2y)(6x - 2y)

since each factor can be factored still further. To factormeans to factor completely, so that each polynomial factor isprime.