Find all the zeros of the function and write the polynomial as a product of linear factors. X⁴ + 13x² + 36 A)±3i,±2i; (x + 3i)(x - 3i)(x + 2)(x - 2) B)±3i,±2i; (x + 3i)(x - 3i)(x + 2i)(x - 2i) C)-3i,-2i; (x - 3i)(x - 3i)(x - 2i)(x - 2i) D)3i,2i; (x + 3i)(x + 3i)(x + 2i)(x + 2i) E)±3i,±2i; (x + 3)(x - 3)(x + 2i)(x - 2i)

Question

Quizplus · Accepted Answer

We can factor out a common factor of (x + 3i)(x - 3i) to get:

(x + 3i)(x - 3i)(xS1U1P2S1S1P0 + 4)

Then, we can use the quadratic formula to solve for the remaining factor:

xS1U1P2S1S1P0 + 4 = 0
xS1U1P2S1S1P0 = -4
x = ±2i

Therefore, the zeros of the function are ±3i and ±2i, and the polynomial can be written as:

(x + 3i)(x - 3i)(x + 2i)(x - 2i)

Find All the Zeros of the Function and Write the Polynomial