Unit: Wrapping Up 5-4: Factoring Quadratic Expressions Essential Question: How do we factor when the first term isn’t simply “x”? Will animations help.

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Presentation transcript:

Unit: Wrapping Up 5-4: Factoring Quadratic Expressions Essential Question: How do we factor when the first term isn’t simply “x”? Will animations help you remember?

5-4: Factoring Quadratic Expressions Sometimes, difficult factorization becomes easy if you take out a GCF first. Factor: 3x x + 36 ▫ Take out the GCF (3) ▫ 3(x 2 + 7x + 12)  Two numbers that multiply together to get 12 and add together to get 7? 3 & 4 ▫ 3(x + 3)(x + 4)

: Factoring Quadratic Expressions Factor: ▫ Outside numbers multiply together ▫ ▫ Middle number is what you’re adding to ▫ ▫ Use the two numbers to split the term in the middle  3x 2 – 16x + 5 ▫ 3x 2 x x + 5 ▫ Now, factor out GCFs out from each half 3 x2x2 – 16 x + 5 = What numbers multiply together to get 15 and add to get -16? -15 and -1

5-4: Factoring Quadratic Expressions 3x 2 – 15x – 1x + 5 ( )( ) (3x 2 – 15x) + (–1x + 5) 3x(x – 5) –1 (x – 5) –1 3x x – 5 x – 5

5-4: Factoring Quadratic Expressions Using guess & check Factor 2x 2 – x – 6 ▫ Write your parenthesis  ( )( ) ▫ How can you break up 2x 2 ?  (2x )(x ) ▫ How can you break up -6?  +1 and -6-1 and +6  +2 and -3-2 and +3 ▫ Try all possibilities, use the “OI” trick to test

5-4: Factoring Quadratic Expressions Factor: 2x 2 – x – 6 What we know: (2x )(x ) What we’re testing: 1/-6, -1/6, 2/-3, -2/3 A hint: ▫ If you’ve already pulled the GCF out, then there should be no GCF in any of the parenthesis RegularReversed (2x + 1)(x – 6)(x + 1)(2x – 6) (2x – 1)(x + 6)(x – 1)(2x + 6) (2x + 2)(x – 3)(x + 2)(2x – 3) (2x – 2)(x + 3)(x – 2)(2x + 3)

5-4: Factoring Quadratic Expressions Using guess & check (an easier one) Factor 2x 2 – 11x + 5 ▫ Write your parenthesis  ( )( ) ▫ How can you break up 2x 2 ?  (2x )(x ) ▫ How can you break up + 5?  +1 and +5-1 and -5 ▫ Which combination are we obviously using?  (2x – 1)(x – 5)(2x – 5)(x – 1)

5-4: Factoring Quadratic Expressions Homework ▫ Worksheet  Put your work on a separate piece of paper  Only do problems where the first term is not simply “x 2 ”  R EMEMBER TO FACTOR OUT A GCF BEFORE TRYING TO FACTOR !! (P ROBLEM #3)