(of the form x 2 + bx + c)
2x(3x – 5)
EXPAND FACTOR
= 6x 2 – 10x
FACTORED FORM Example:
5x(x + 5)
(x + 2)(x + 5)
(x – 2)(x + 2)
To factor a polynomial means to express it as a product
(ie) the reverse of expanding.
EXPANDED FORM
5x 2 + 25x
x 2 + 7x + 10
x 2 – 4
FACTORING CHECKLIST
1.
Greatest Common Factor (GCF)
 the polynomial must have 2 or more terms
 there must by a GCF between all the terms
 the GCF can be a number, a variable, or both
Example: 5x + 25
2.
Simple Trinomial
 the polynomial must have only three terms
 the numerical coefficient of x 2 must be equal to one ( a = 1)
 use the product & sum rule
Example: x 2 + 7x + 12 Product & Sum Rule:
To factor a simple trinomial, x 2 + bx + c, determine two integers that:
 have a sum of b
 have a product of c
Unit 3 Lesson3 Page 1 of 2

3. Difference of Squares
 the polynomial must have only 2 terms
 there must be a subtraction sign that separates the two terms
 both terms must be perfect squares
Example: x 2 – 25 Difference of Squares:
x 2 – y 2 = (x – y)(x + y)
FACTORING DECISION TREE check for GCF simple trinomial
(3 terms) difference of squares
(2 terms)
x 2 + bx + c
(sum of b, product of c)
x 2 – y 2 = (x – y)(x + y)
________________________________________________
Example  Factor each of the following, if possible: a) 4x + 12 b) 5x 2 + 30x c) 14x – 5y d) x 2 + 7x + 10 e) w 2 – 6w + 5 f) m 2 – m – 42 g) x 2 + 10x + 25 (perfect square trinomial) h) x 2 – 49 i) b
2
– 25 j) h
2
+ 81
(*any answer can be checked by re-expanding*)
Unit 3 Lesson3 Page 2 of 2