CHAPTER_ppt_6_4 - = x (2 x + 1) + 4(2 x + 1) = (2 x + 1)( x...

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§ 6.4 Factoring Trinomials of the Form x 2 + bx + c by Grouping
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Martin-Gay, Beginning and Intermediate Algebra, 4ed 2 To Factor Trinomials by Grouping 1) Factor out a greatest common factor, if there is one other than 1. 2) For the resulting trinomial ax 2 + bx + c , find two numbers whose product is a · c and whose sum is b . 3) Write the middle term bx , using the factors found in Step 2. 4) Factor by grouping. Factoring by Grouping
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Martin-Gay, Beginning and Intermediate Algebra, 4ed 3 Factoring by Grouping Example : Factor by grouping: 2 x 2 + 9 x + 4 Find two numbers that we can multiply together to get 8 and add together to get 9. ___ × ___ = 8 ___ + ___ = 9 1 1 8 8 The value of ac = 8. Rewrite 9 x as x + 8 x . 2 x 2 + 9 x + 4 = 2 x 2 + x + 8 x + 4 Factor by grouping.
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Unformatted text preview: = x (2 x + 1) + 4(2 x + 1) = (2 x + 1)( x + 4) Check : (2 x + 1)( x + 4) = 2 x 2 + 8 x + 1 x + 4 = 2 x 2 + 9 x + 4 Factor out (2 x + 1). Martin-Gay, Beginning and Intermediate Algebra, 4ed 4 Factoring by Grouping Example : Factor by grouping: 8 x 2 + 10 x-3 (2 x + 3)(4 x-1) = 8 x 2 + 10 x-3 Check: Find two numbers that we can multiply together to get -24 and add together to get 10. ____ ____ = -24 ____ + ____ = 10 12 12 (-2) (-2) The value of ac is -24. Rewrite 10 x as 12 x + (-2 x ). 8 x 2 + 10 x-3 = 8 x 2 + 12 x-2 x-3 Factor by grouping. = 4 x (2 x + 3) -1(2 x + 3) = (2 x + 3)(4 x-1) Factor out (2 x + 3)....
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CHAPTER_ppt_6_4 - = x (2 x + 1) + 4(2 x + 1) = (2 x + 1)( x...

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