SOLUTION: Factor the following and list all zeros (roots): x^4+7x^3-4x^2-52x+48

Question 392537: Factor the following and list all zeros (roots):
x^4+7x^3-4x^2-52x+48
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Using the rational root test, x=1 and x=2 are zeros of the polynomial, so (x-1)(x-2) or divides the polynomial. Dividing using long division or synthetic division twice, we get , so the polynomial is equal to . The first expression has roots at 1 and 2 (we've already figured this), and the other expression factors to (x+6)(x+4) so it has roots at -6 and -4. Therefore the four roots are 1,2, -4, -6 and the factorization is

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