third degree, real coefficients, y-intercept is -52, two zeros are -1 and 5+i.
If a polynomial has real coefficients, its complex are conjugate. A polynomial of the third degree with zeros -1, 5+i, and 5 - i has the form: p(x) = A(x +1)(x - 5 - i)(x - 5 + i) = A(x+1)((x-5)^2 + 1) = A(x+1)(x^2 - 10x + 26).
Since p(0) = -52, we have 26A = -52 or A = -2.
Finally, p(x) = -2(x+1)(x^2 - 10x + 26) = -2(x^3 - 9x^2 + 16x + 26) = -2x^3 + 18x^2 - 32x - 52.
I had to study it for a few minutes. But I have it now, thank you so much for your help!
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