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Is the indicated complex number a zero of the polynomial function f ? 1 + 2 i ; f ( x ) = x 4

Is the indicated complex number a zero of the polynomial functionf?1 +2i;f(x) =x42x311x2+32x80

Use the Conjugate Zeros Theorem and other techniques to find all other zeros. (If there are no other zeros, enter NA. Enter your answers as a comma-separated list.)

x=

Give the complete factorization off(x).

f(x) =

Use Descartes's rule of signs to state the number of possible positive and negative real roots. (Enter your answers as a comma-separated list.)x4+2x320x22x+21= 0

number of possible positive real roots:

number of possible negative real roots:

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