The polynomial function P(x) has degree 4 and a leading coefficient of -2. The Zeros are 4, -1, and 3i.

Question

The polynomial function P(x) has degree 4 and a leading coefficient of -2. We know that three of the Zeros are 4, -1, and 3i. Write the polynomial function in standard form, that is, multiply out the linear factors!

P(x)= _________________

Hint: Imaginary Zeros appear in conjugate pairs!

Answer 1

P(x) =-2(x-4)(x+1)(x+3i)(x-3i)

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

=-2(x^4-3x^3+5x^2-27x-36)

=-2x^5 +6x^3 -10x^2+54x +72