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(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