How do you factor by grouping four-term polynomials and trinomials?
1 Answer
Factoring by grouping involves grouping terms then factoring out common factors. Here are examples of how to factor by grouping:
Example with trinomial:
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To use grouping method you need to multiply
#ax^2# and#c# , which is#-36x^2# in this example. Now you need to find two terns that multiplied gives you#-36x^2# but add to -16x. Those terms are -18x and 2x. We now can replace#bx# with those two terms:
#3x^2 - 16x - 12#
#3x^2 - 18x + 2x - 12# -
Group the expression by two:
#(3x^2 - 18x) + (2x - 12)# -
Factor out GCF in each group:
#3x(x - 6) + 2(x - 6)#
(The binomials in parentheses should be the same, if not the same... there is an error in the factoring or the expression can not be factored.) -
The next step is factoring out the GCF which basically has you rewrite what is in parentheses and place other terms left together:
#(x - 6)(3x +2)# (THE ANSWER)
Example with polynomial:
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Group the expression by two:
#(xy - 3x) - (6y - 18)#
Careful with the sign outside before parenthesis.. changes sign of the 18. -
Factor out GCF in each group:
#x(y - 3) - 6(y - 3)#
(The binomials in parentheses should be the same, if not the same... there is an error in the factoring or the expression can not be factored.) -
The next step is factoring out the GCF which basically has you rewrite what is in parentheses and place other terms left together:
(y - 3)(x - 6) (THE ANSWER)