Consider the following Px x4 x3 3x2 9x 108 Find all the z

Consider the following. P(x) = x4 + x3 3x2 + 9x 108 Find all the zeros of the polynomial function. (Hint: First determine the rational zeros. Enter your answers as a comma-separated list. Enter all answers including repetitions.)

x =

Write the polynomial as a product of its leading coefficient and its linear factors.

P(x) =

Solution

P(x) = x⁴ + x³ 3x² + 9x 108

= (x -3)(x + 4)(x + 3i)(x - 3i)

P(x) = 0

x = 3, -4, 3i, -3i