Unit 3 Factoring: 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: 18x 3 – 24x x Always Look for Common Factors First!

Simple Trinomial Factoring Recall: general form of quadratic y = ax 2 + 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 = x 2 + 3x + 2x + 6 y = x 2 + 5x + 6

Factor: x 2 + 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 x 2 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: 2x x + 12 Always Look for Common Factors First!

Practice Factor a)y = x 2 + 4x + 3 a)y = x 2 – 10x + 9 a)y = x 2 – x – 20 a)y = 2x 2 – 4x + 2 a)y = 5x 2 – 40x + 80 a)y = 4x 2 – 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 FormFactored FormVertex Form y = ax 2 + 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!