The polynomial function P(x) has degree 4 and a leading coefficient of 3. The Zeros are -5, 2, and 4i.

Question

The polynomial function P(x) has degree 4 and a leading coefficient of 3. We know that three of the Zeros are -5, 2, and 4i. 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

Hi,

Since we know the leading coefficient, zeroes and degree of the polynomial, we can write it as

P(x)= 3 (x-(-5)((x-2) (x-4i)(x+4i).

Since 4i is a zero, then -4i will be a zero as well. Now the only thing left is to simplify the expression.

Best wishes,

Bsh