Unit 3Factoring: Common and Simple Trinomial

LG: I can write quadratic equations in factored form using common factoring

and simple trinomial factoring

Recall: Distributive Property• Term outside of brackets is multiplied by all terms

inside brackets General Form: a(b + c) = ab + ac

Now: Common Factoring (reverse of distributive property)

• Determine the largest factor (number and/or variable) that divides into each term.

General Form: ab + ac = a(b + c)

Common Factoring: Examples

• Ex. 1: 5x - 15 • Ex. 2: 21y – 28x• Ex. 3: 10x – 15y – 30• Ex. 4: 18x3 – 24x2 + 12x

Always Look for Common

Factors First!

Simple Trinomial Factoring• Recall: general form of quadratic y = ax2 + bx + c• Simple Trinomial Factoring – can be used when a = 1 or

‘a’ can be removed by common factoring.– STF is like FOIL in reverse

• Example: y = (x + 3) (x + 2) y = x2 + 3x + 2x + 6y = x2 + 5x + 6

Factor:x2 + 7x + 6 = (x + ____ ) (x +

____ )

– To factor a simple trinomial, we need to find two numbers that add to give ‘b’ and multiply to give ‘c’

– Because the coefficient of x2 is 1, we know that the coefficient of x in each binomial is 1.

– The same equation could be disguised by including a common factor:2x2 + 14x + 12 Always Look for

Common Factors First!

Practice

Factora) y = x2 + 4x + 3

b) y = x2 – 10x + 9

c) y = x2 – x – 20

d) y = 2x2 – 4x + 2

e) y = 5x2 – 40x + 80

f) y = 4x2 – 24x + 36

Always Look for Common

Factors First!

Consolidation

Why bother factoring???

Remember…• There are THREE different forms of the

QUADRATIC EQUATION

• Each is uniquely useful!• What info does factored form tell us?

Standard Form Factored Form Vertex Form y = ax2 + bx + c y = a(x – s)(x – t) y = a(x – h)2 + k

Homework

• Pg. 230 # 6a-f• Pg. 298 # 5a-e• Pg. 307# 2, 3

• Quiz Tomorrow!– Identifying Quadratic Relations (equation, graph, table of

values)– Special Features of Parabolas– Distributive property and exponent laws– FOIL

Always Look for Common

Factors First!