SOLUTION: 7x2+17x+6 factoring trinomials of the form ax2+bx+c

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Question 67711: 7x2+17x+6
factoring trinomials of the form ax2+bx+c
Found 2 solutions by stanbon, prabhjyot:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
7x^2+17x+6
Think of two numbers whose product is 7*6=42
and whose sum is 17.
The numbers are 3 and 14.
Replace 17x with 14x+3x to get:
=7x^2+14x+3x+6
Factor the 1st two and the last two terms separately to get:
=7x(x+2)+3(x+2)
Factor out the common factor to get:
=(x+2)(7x+3)
Cheers,
Stan H.

Answer by prabhjyot(165) About Me  (Show Source):
You can put this solution on YOUR website!
7x%5E2%2B17x%2B6
Equation:
a = 7
b = 17
c = 6

Discriminant: %28b%5E2-4ac%29 =%28+17%5E+2-4%2A7%2A6%29 = 121+%29
Discriminant (121) is greater than zero. The equation has two solutions.
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+


or
x+=+%28-17+%2B-+sqrt%28+17%5E2-4%2A7%2A6+%29%29%2F%282%2A7%29+
or
x1,2 = (-17 ± 11) / 2*7
or
x1 = -6 / 14 = -3/7
x2 = -28 / 14 = -2
or
x1,2 = -0.42, -2
Expression factored: %287x%5E2%2B17x%2B6%29 = %287%28x%2B0.42%29%28x%2B2%29%29