6.4? Factoring Trinomials and

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6.4? Factoring Trinomialsand
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Lets Investigate(x 4)(x 3 ) x2 3x 4x
12 x2 7x 21
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(x 4)(x 3) x2 3x 4x 12 x2 7x
12Factor x2 7x 12
What set of factors of 12 add up to 7
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Factoring by grouping using the
diamond method
Use the numbers in the left and right of your
diamond as your x coefficients to make a 4-term
polynomial x2 3x 4x 12 Group the first two
terms together and the last two terms
together (x2 3x) (4x 12) Factor out the GCF
of each group x(x 3) 4(x 3) Notice that the
contents of the parentheses are the same! Use
that group as one set of parentheses, and then
take the GCF's and put them in a set of
parentheses (x 3)(x 4) Voila! You've
factored the polynomial!
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Factoring the bottoms-up way using the diamond
method
Set up two sets of parentheses as shown below
using the left and right numbers in the
diamond (__x 3)(__x 4) Divide both of the
numbers by a (__x 3)(__x 4)
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1 Bottoms-up! Simplify... (x 3)(x 4) Done!
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Now...the bottoms-up method
Same equation...6x2 13x 6 (__ x 9)(__x
4) (__ x 9)(__x 4)
6 6 Reduce... (__ x
3)(__x 2)
2 3 Bottoms-up! (2x 3)(3x
2) Done!
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Factor using your favorite method 3x2 4x 1
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Factor using your favorite method 8x2 - 6x - 9
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APage 276 1 36(show the diamond method)