Lesson26 - . It puts the trinomial back as the product of...

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1 Lesson 26, Sections 5.3 and 5.4 (part 1) Factoring out the Greatest Common Factor, Factoring by Grouping Factoring Trinomials (part 1) Factoring out the GCF is reversing the ‘distributive property’ . It is putting the polynomial back as a product (multiplied). Factor each polynomial by factoring out the GCF. 1) 2 3 4 6 8 x x x - + 2) b a b a 3 2 2 9 3 + 3) n m m 3 2 12 4 - - 4) ab y x - - 2 2 5) 2 16 8 4 x mn xm - + Write an equivalent function by factoring. 6) 4 5 9 3 ) ( x x x f - - = 7) 4 5 4 ) ( t t t G - =
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2 Sometimes the GCF may be a ‘grouping’ (parentheses). Factor out the GCF. 8) 4( 2 ) 3 ( 2 ) x y a x y + - + = 9) (3 1)( 2) (2 4)( 2) x x x x + - + - - = Factoring by Grouping can often be used with a polynomial with 4 terms. Here is an example: Factor 2 8 3 12 ax a x - + - 2 8 3 12 Group the first 2 terms together, then the last 2 terms together. Factor the GCF from each pair. Look for a 'match'. 2 ( 4) 3( 4) ( 4)(2 3) ax a x a x x x a - + - = - + - = - + 10) ab ac bd cd + - - = 11) 2 2 2 12 24 x nx n - - + = 12) 2 3 6 18 rm m rm - + - =
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3 Factoring a trinomial often is reversing ‘FOIL’
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Unformatted text preview: . It puts the trinomial back as the product of two binomials. Form: c bx x + + 2 Always write terms in descending order! Notice: 15 2 15 3 5 ) 5 )( 3 ( 2 2-+ =--+ = +-x x x x x x x-15 is the product of -3 and 5 2 is the sum of -3 and 5 If a trinomial is of the form c bx x + + 2 , find a pair of numbers r and s ; such that the product ( r )( s ) equals c and the sum r + s equals b . Then the factors are ) )( ( s x r x + + . You must watch signs!!! Factor the following. 1) 5 6 2 + + x x Find a pair of numbers with a product of 5 and a sum of 6. 2) 50 20 2 2 +-a a Notice you can take out a GCF of 2 first. ) 25 10 ( 2 2 +-= a a Now, find a pair of numbers with a product of 25 and a sum of -10. 3) a a a 72 2 3--4) 10 3 2-+ x x 5) 2 56 x x-+ Hint: Factor out a GCF of -1 first....
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Lesson26 - . It puts the trinomial back as the product of...

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