SOLUTION: {{{ x^3-13x+12=0 }}} find the answers of x without using a calculator and please if you have a way to solve the cubic equations put it i still have 30 more to go

Question 1057009: find the answers of x without using a calculator and please if you have a way to solve the cubic equations put it i still have 30 more to go
Found 2 solutions by josgarithmetic, solve_for_x:
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
Did Rational Roots Theorem with synthetic division help you?
Answer by solve_for_x(190) (Show Source): You can put this solution on YOUR website!
Unfortunately, the direct solution formula for a cubic equation is very, very ugly.

The better way to solve something like this is to find one solution that works, and
then use that to factor a term out of the expression, which will reduce the rest of
it to a quadratic expression. You can then either factor the quadratic, or use the
quadratic formula.

For this problem, it is pretty easy to see that x = 1 will be a solution, since it gives:

1 - 13(1) + 12 = 0
1 - 13 + 12 = 0
-12 + 12 = 0
0 = 0

Since x = 1 is a solution, you know that (x - 1) is a factor.

Using polynomial division, divide by (x - 1), to get:

Thus,

Next, factor to get

This means that:

And from the factors on the right hand side, you can see that
the solutions are -4, 1, and 3.
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