Algebra Tutorials! Home Solving Quadratic Equations by Completing the Square Graphing Logarithmic Functions Division Property of Exponents Adding and Subtracting Rational Expressions With Like Denominators Rationalizing the Denominator Multiplying Special Polynomials Functions Solving Linear Systems of Equations by Elimination Solving Systems of Equation by Substitution and Elimination Polynomial Equations Solving Linear Systems of Equations by Graphing Quadratic Functions Solving Proportions Parallel and Perpendicular Lines Simplifying Square Roots Simplifying Fractions Adding and Subtracting Fractions Adding and Subtracting Fractions Solving Linear Equations Inequalities in one Variable Recognizing Polynomial Equations from their Graphs Scientific Notation Factoring a Sum or Difference of Two Cubes Solving Nonlinear Equations by Substitution Solving Systems of Linear Inequalities Arithmetics with Decimals Finding the Equation of an Inverse Function Plotting Points in the Coordinate Plane The Product of the Roots of a Quadratic Powers Solving Quadratic Equations by Completing the Square
Try the Free Math Solver or Scroll down to Tutorials!

 Depdendent Variable

 Number of equations to solve: 23456789
 Equ. #1:
 Equ. #2:

 Equ. #3:

 Equ. #4:

 Equ. #5:

 Equ. #6:

 Equ. #7:

 Equ. #8:

 Equ. #9:

 Solve for:

 Dependent Variable

 Number of inequalities to solve: 23456789
 Ineq. #1:
 Ineq. #2:

 Ineq. #3:

 Ineq. #4:

 Ineq. #5:

 Ineq. #6:

 Ineq. #7:

 Ineq. #8:

 Ineq. #9:

 Solve for:

 Please use this form if you would like to have this math solver on your website, free of charge. Name: Email: Your Website: Msg:

# Factoring Polynomials

A strategy for factoring polynomials is given in the following box.

Strategy for Factoring Polynomials

1. If there are any common factors, factor them out first.

2. When factoring a binomial, look for the special cases: difference of two squares, difference of two cubes, and sum of two cubes. Remember that a sum of two squares a2 + b2 is prime.

3. When factoring a trinomial, check to see whether it is a perfect square trinomial.

4. When factoring a trinomial that is not a perfect square, use grouping or trial and error.

5. When factoring a polynomial of high degree, use substitution to get a polynomial of degree 2 or 3, or use trial and error.

6. If the polynomial has four terms, try factoring by grouping.

Example

Using the factoring strategy

Factor each polynomial completely.

a) 3w3 - 3w2 - 18w

b) 10x2 + 160

c) 16a2b -80ab + 100b

d) aw + mw + az + mz

Solution

a) The greatest common factor (GCF) for the three terms is 3w:

 3w3 - 3w2 - 18w = 3w(w2 - w - 6) Factor out 3w. = 3w(w - 3)(w + 2) Factor completely.

b) The GCF in 10x2 + 160 is 10:

10x2 + 160 = 10(x2 + 16)

Because x2 + 16 is prime, the polynomial is factored completely.

c) The GCF in 16a2b - 80ab + 100b is 4b:

 16a2b - 80ab + 100b = 4b(4a2 - 20a + 25) = 4b(2a - 5)2

d) The polynomial has four terms, and we can factor it by grouping:

 aw + mw + az + mz = w(a + m) + z(a + m) = (w + z)(a + m)