degree 3, zeros of 3𝑖 and −3, and a y-intercept of (0,−12).

Question

Create a polynomial 𝑝 with real number coefficients that has degree 3, zeros of 3𝑖 and −3, and a y-intercept of

(0,−12). Expand (multiply out the factors of) your polynomial to write the final answer as a polynomial whose

terms appear in descending order.

Answer 1

x=3i

x^2 =-9

x^2+9 = 0

x^2+9 is one factor

x=-3

x+3 =0

the other factor is x+3

multiply the two factors together

p(x) = (x+3)(x^2+9)

= x^3 +3x^2 +9x +27

but y intercept =-12, not +27

so

p(x) = (-12/27)(x^3 +3x^2 +9x +27)

= -(4/9)(x^3 +3x^2 +9x +27)

= -4x^3/9-4x^2/3 -4x -12

= (-4/9)x^3 -(4/3)x^2 -4x -12 has y intercept =-12 and zeros -3 and 3i