SOLUTION: Factor to find all the zeros x^3-5x^2+16x-30=0

Question 807106: Factor to find all the zeros x^3-5x^2+16x-30=0
Answer by tommyt3rd(5050) (Show Source): You can put this solution on YOUR website!
factors of 30:

1,2,3,5,15,30
of which we'd determine that x=3 is a solution such that
x^3-5x^2+16x-30=(x-3)(x^2-2x+10)=0
but the quadratic is not factorable over the reals - so we'd need the quadratic formula to determine that x=1+3i, and x=1-3i are the other two factors. Thus the zeros are:
{3, 1-3i, 1+3i}
RELATED QUESTIONS
Factor to find all the real zeros of P(x)=... (answered by jsmallt9)

Use the rational zeros theorem to find all the real zeros of the polynomial function. Use (answered by josgarithmetic)

Use the rational zeros theorem to find all the real zeros of the polynomial function. Use (answered by lwsshak3)

Find all rational zeros and factor f(x).... (answered by Nate)

how to find all the zeros for 4x^4-x^3+5x^2-2x-6 (answered by stanbon)

A polynomial P is given. P(x) = x^4 + 18x^2 + 81 (a) Factor P into linear and... (answered by MathLover1)

f(x)=x^3+2x^2-5x-6 find the real zeros of "f"? X= use the real zeros to factor "f" (answered by stanbon)

use the rational zeros theorem to find all zeros of the polynomial. Use the zeros to... (answered by josgarithmetic)