Find a formula for the polynomial P(x)

Question

Find a formula for the polynomial P(x) with

• degree 3

• real coefficients

zeros at 4-i and x = -4

• y-intercept at (0, -136)

P(x) =

Answer 1

x=4-i

x=-4

x+4=0

x+4 = one factor

x-4 =-i

x^2-8x +16 = -1

x^2-8x +17 = 0

x^2-8x+17 is the other factor

multiply them together to get the 3 degree polynomial

P(x) = a(x+4)(x^2-8x+17)

= a(x^3 -4x^2 -15x + 68)

to get -136 instead of 66 for the y intercept

a =-136/68

P(x) = (-136/68)x^3 +136x^2/17 + 136(15)x/88 - 136