Use the given zero end synthetic division to determine all o

Use the given zero end synthetic division to determine all of the zeros of P(x). Then factor the depressed equation to write P(x) as a product of the linear factors. P(x) = x^2 + (3i - 5)x - 15i, x = -3i P(x) = (Type your answer in factored form. Express complex numbers in terms of i.)

Solution

P(x) =x^2 +3ix -5x -15i

Using sythetic division : Divide ( x^2 +3ix -5x -15i)/(x +3i)

-3i || 1 3i -5    -15i

              -3i             15i

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      1          -5           0

So, x -5 is one root

So, P(x) = (x+3i)(x +5)