SOLUTION: How to factor Trinomials of the form ax^2+bx+c

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Question 260329: How to factor Trinomials of the form ax^2+bx+c
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
To factor trinomials of this form:
step 1 - factor out the a from the first two terms to get
a%28x%5E2+%2B+%28b%2Fa%29x%29+%2B+c
step 2 - take 1/2 of the middle term and square it. We get
a%28x%5E2+%2B+%28b%2Fa%29x+%2B+%28b%2F2a%29%5E2%29+%2B+c
step 3 - place a blank slot after c and we get
a%28x%5E2+%2B+%28b%2Fa%29x+%2B+%28b%2F2a%29%5E2%29+%2B+c+-+_____+
this blank slot is waiting for a number.
step 4 - multiply (b/2a)^2 by a and put that answer in the blank slot to get
a%28x%5E2+%2B+%28b%2Fa%29x+%2B+%28b%2F2a%29%5E2%29+%2B+c+-+b%5E2%2F%284a%29
step 5 rewrite the trinomial as a binomial squared as
a%28x%2B%28b%2F%282a%29%29%29%5E2+%2B+%284ac-b%5E2%29%2F%284a%29
we have our factored form for x.