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	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
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	Arithmetics with Decimals
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	Plotting Points in the Coordinate Plane
	The Product of the Roots of a Quadratic
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	Solving Quadratic Equations by Completing the Square

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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)

Helpful hint

When factoring integers, we write 4 = 2 Â· 2. However, when factoring polynomials we usually do not factor any of the integers that appear. So we say that 4b(2a - 5)² is factored completely.