so i think find the zeros means to find the roots right? so would i do the whole integral roots thereom thing then factor? i should end up with 3 roots right?
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Yes, the zeros and roots are the same thing. Yes and yes.
Look at the graph or use the rational roots theorem to find the root at x = -5.
Use the factor theorem to convert this root into a factor:
(x + 5)
Divide by the known factor:
(x^3+9x^2+26x+30) / (x + 5) = x^2 + 4x + 6
This reduced quadratic has no real or rational roots. If you need to find the remaining two complex roots, use the quadratic formula.
The only real root of the original cubic is x = -5.
Look at the graph or use the rational roots theorem to find the root at x = -5.
Use the factor theorem to convert this root into a factor:
(x + 5)
Divide by the known factor:
(x^3+9x^2+26x+30) / (x + 5) = x^2 + 4x + 6
This reduced quadratic has no real or rational roots. If you need to find the remaining two complex roots, use the quadratic formula.
The only real root of the original cubic is x = -5.