# algebra

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solve the following in the real number system
x^3 + 8x^2 + 10x - 15 = 0

• algebra -

Since it is hard to factor a general cubic, look for easy roots. They will be among ±1,3,5,15

A little synthetic division shows that we have
(x+3)(x^2 + 5x - 5)

Now you can use the quadratic formula to get the other two roots:

(-5 ± 3√5)/2

• algebra -

by inspection, x=-3 is a solution.
-27+72-30-15=0

so, divide (x+3) into x^3+8x^2+10x-15 and get the quadratic. Then solve it with the quadratic equation.

I get x^2+5x-5 check that.

• algebra -

Thank you I think I understand it better with Bob's answer.

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