SOLUTION: Find all the roots of p(x)=x^4+4x^3-x^2-16x-12

Question 1113622: Find all the roots of p(x)=x^4+4x^3-x^2-16x-12
Found 2 solutions by ikleyn, josgarithmetic:
Answer by ikleyn(52776) (Show Source): You can put this solution on YOUR website!
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Plot y = The roots are -3, -2, -1 and 2. You can check it manually. The rational root theorem says that the rational / integer roots are anomg the divisors of the constant term "-12", and voila: they all are there ! The plot visualizes them momentarily !

Answer by josgarithmetic(39616) (Show Source): You can put this solution on YOUR website!
The possible roots to test are -12, -6, -4, -3, -2, -1, 1, 2, 3, 4, 6, 12.

The roots will be found -3, -2, -1, 2.
You could use synthetic division to check each possible root and continue with the resulting quotient, to continue checking for the possible roots.

Just one example.

-3 | 1 4 -1 -16 -12 | | -3 -3 12 12 |------------------------------ 1 1 -4 -4 0

Remainder of 0;
The next polynomial to check roots of is
but now the possible roots to check are now -4,-2,-1,1, 2, 4.

All the roots found will be -3, -2, -1, 2.
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