We will find a polynomial of third degree with zeros: -2 and 4 + i and y-intercept in −68.

Since 4 + i is one of the zeros follows 4 - i is also a zero (complex roots come in complex conjugate pairs)

The general form of the polynomial is:

y = a(x - x1)(x - x2)(x - x3), where x1, x2 and x3 are the roots and a is a constant

In our case 

x1 = -2

x2 = 4 + i

x3 = 4 - i

y = a(x - (-2))(x - (4 + i))(x - (4 - i))

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click here to see the step by step simplifying

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y = a(x^3 - 6x^2 + x + 34)

Since y intercept is - 68 this means for x = 0 we have y = - 68:

a(0^3 - 6*0^2 + 0 + 34) = -68

a = -68/34

a = -2

The polynomial of third degree is:

y = (-2)(x^3 - 6x^2 + x + 34)

y = -2x^3 + 12x^2 - 2x - 68