Unit: Wrapping Up5-4: Factoring Quadratic ExpressionsEssential 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: 3x2 + 21x + 36▫Take out the GCF (3)▫3(x2 + 7x + 12)

Two numbers that multiply together to get 12 and add together to get 7? 3 & 4

▫3(x + 3)(x + 4)

-1-15

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5-4: 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 3x2 – 16x + 5

▫3x2 x x + 5▫Now, factor out GCFs out from each half

3x2 – 16 x+5=15

-16What numbers multiply together to get 15 and add to get -16?-15 and -1

5-4: Factoring Quadratic Expressions•3x2 – 15x – 1x + 5• • • ( )( )

(3x2 – 15x) + (–1x + 5)3x(x – 5) –1 (x – 5)–13x x – 5 x – 5

5-4: Factoring Quadratic Expressions•Using guess & check•Factor 2x2 – x – 6▫Write your parenthesis

( )( )▫How can you break up 2x2?

(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: 2x2 – 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

Regular Reversed(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 2x2 – 11x + 5▫Write your parenthesis

( )( )▫How can you break up 2x2?

(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 “x2” REMEMBER TO FACTOR OUT A GCF BEFORE

TRYING TO FACTOR!! (PROBLEM #3)