+128474 x^3 + 2x^2 - 7x - 2
We have something called the Rational Roots Theorem here that might help us....without going into detail ...the possible rational roots are 1, - 1 , 2 or -2
I see that 1 is not a root
I see that -1 isn't either
But 2 is a root because (2)^3 + 2(2)^2 -7(2) - 2 = 8 + 8 - 14 - 2 = 0
So....using synthetic division, we can find the remaining polynomial
2 [ 1 2 - 7 -2 ]
2 8 2
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1 4 1 0
The remaining polynomial is x^2 + 4x + 1
We can complete the square on x to find the other two roots
x^2 + 4x + 4 = - 1 + 4
(x + 2)^2 = 3 take both roots
x + 2 = ±√ 3 subtract 2 from both sides and we get the other two solutions
x = √3 - 2 or x = -√3 - 2
