SOLUTION: factoring complex trinomials: 10x^2+19x-15

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Question 1204135: factoring complex trinomials: 10x^2+19x-15
Found 3 solutions by mananth, MathLover1, ikleyn:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!

factoring complex trinomials: 10x^2+19x-15
10*-15 =-150
split 19 into two parts such that when you add the parts you get 19 and when you multiply them you get -150
+25 &-6 are the terms
10x^2 +25x-6x-15
5x(2x+5)-3(2x+5)
(2x+5)(5x-3)

Answer by MathLover1(20850) About Me  (Show Source):
Answer by ikleyn(52915) About Me  (Show Source):
You can put this solution on YOUR website!
.
factoring highlight%28cross%28complex%29%29 highlight%28cross%28trinomials%29%29 trinomial: 10x^2+19x-15
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Use the quadratic formula and find the roots of this trinomial

    x%5B1%2C2%5D = %28-19+%2B-+sqrt%2819%5E2+-+4%2A10%2A%28-15%29%29%29%2F20 = %28-19+%2B-+31%29%2F20.


The roots are  x%5B1%5D = %28-19+%2B+31%29%2F20 = 12%2F20 = 3%2F5,

               x%5B2%5D = %28-19+-+31%29%2F20 = -50%2F20 = -5%2F2.


Hence, factoring is

    10x^2 + 19x - 15 = 10%2A%28x-x%5B1%5D%29%2A%28x-x%5B2%5D%29 = 10%2A%28x-3%2F5%29%2A%28x%2B5%2F2%29 = (5x-3)*(2x+5).    ANSWER

Solved.

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On solving quadratic equations using the quadratic formula,  see the lessons
    - Introduction into Quadratic Equations
    - PROOF of quadratic formula by completing the square
in this site.


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