The polynomial function P(x) has degree 4 and a leading coefficient of -2. Write the polynomial function in standard form,

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

We know that the 4 zeros are 4, -2, 3i and -3i

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

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

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

P(x) = -2x^4 + 6x^3 - 10x^2 + 54x + 72

Answer 2

P(x) = -2(x - 4)(x - -1)(x-3i)(x-(-3i))= -2(x-4)(x+1)(x-3i)(x+3i) = -2(x² -3x -4)(x² + 9)

Multiply out to get the final answer