We can actually go one more step here and factor a 2

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Unformatted text preview: has more than one pair of positive factors. This means that the initial form must be one of the following possibilities. ( )( x + ) + 10 x - 6 = ( 2 x + ) ( 2 x + ) 4 x 2 + 10 x - 6 = 4 x + 4x2 To fill in the blanks we will need all the factors of -6. Here they are, ( -1) ( 6 ) (1) ( -6 ) ( -2 ) ( 3 ) ( 2 ) ( -3 ) With some trial and error we can find that the correct factoring of this polynomial is, 4 x 2 + 10 x - 6 = ( 2 x - 1) ( 2 x + 6 ) Note as well that in the trial and error phase we need to make sure and plug each pair into both possible forms and in both possible orderings to correctly determine if it is the correct pair of factors or not. We can actually go one more step here and factor a 2 out of the second term if we’d like to. This gives, 4 x 2 + 10 x - 6 = 2 ( 2 x - 1) ( x + 3) This is important because we could also have factored this as, 4 x 2 + 10 x - 6 = ( 4 x - 2 ) ( x + 3) which, on the surface, appears to be different from the first form given above. However, in this case we can facto...
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This note was uploaded on 06/06/2012 for the course ICT 4 taught by Professor Mrvinh during the Spring '12 term at Hanoi University of Technology.

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