SOLUTION: Explain and demonstrate how to factor a trinomial in the form: ax^2+bx+c with an example where a, b and c are values

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Question 650112: Explain and demonstrate how to factor a trinomial in the form: ax^2+bx+c with an example where a, b and c are values
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

what you are looking for is called expansion and grouping
so, you have to to expand "bx" into two terms, such that one term will have a common factor with a and the other will have a common factor with c
for example:
2x%5E2+-+x+-+3
you are going find numbers that are factors of -6 (these are 2+%2A+-3) ) that add up to -1 (-x+=+-1x)
these factors are -3 and 2
so you would rewrite the equation as:
2x%5E2+%2B+2x+-+3x+-+3 (doing so,you didn't really change anything, because 2+-+3+=+-1, so the integrity of the expression is still there)
now you factor in parts. from the first part, take out 2x, from the second, take out -3
so, you have:
2x%28x+%2B+1%29+-+3%28x+%2B+1%29 . . . . (if you notice, both of the terms in the ()'s are the same, this will always happen if it doesn't, you have done something wrong
then you say:
%282x+-+3%29%28x+%2B+1%29...that's factored
if u multiply this out, you will get back to the original expression of 2x%5E2+-+x+-+3