Lesson 10.5 Factoring Objective: To factor a quadratic trinomial of the form Factoring a trinomial is the opposite of multiplying two binomials. Example:

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Presentation transcript:

Lesson 10.5 Factoring Objective: To factor a quadratic trinomial of the form Factoring a trinomial is the opposite of multiplying two binomials. Example: Factor You need to find two numbers whose sum is 5 and whose product is 6 (x + ? )(x + ? ) 2 and 3 (x + 2)(x + 3) Check by multiplying (x +2)(x + 3)=

EX: Factor Find two numbers that + to get 7  to get 12 (x + 3)(x + 4) 3 and 4 EX: Factor Find two numbers that + to get 4 x to get -12 (x + 6) (x – 2) 6 and –2

Example: Factor Find two numbers that + to get –5  to get 6 –2 and –3 (x – 2)(x – 3) Find two numbers that + to get –7  to get –30 Example: Factor (x – 10)(x + 3) –10 and 3

Solving Quadratic Equations by Factoring EX: Solve for x by factoring. Find two #’s that + to get 8 and x to get 12 2 and 6 (x + 2)(x + 6) = 0 Use zero product property to solve for x. x + 2 = 0 and x + 6 = 0 –2 –2 –6 –6 x = -2 x = -6

EX: Solve for x Numbers that + to get 7, x to get –18 9 and –2 (x + 9)( x – 2) = 0 x + 9 = 0 x – 2 = 0 x = – 9 and 2