Asked by annoymous
Q1: A polynomial P is given.
P(x) = x^5 + 4x^3
a) Find all zeros of P, real and complex. (Enter your answers as a comma-separated list. Enter all answers including repetitions.)
(b) Factor P completely.
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Q2: A polynomial P is given.
P(x) = x^4 − 256
a) Find all zeros of P, real and complex. (Enter your answers as a comma-separated list. Enter all answers including repetitions.)
b) Factor P completely.
P(x) = x^5 + 4x^3
a) Find all zeros of P, real and complex. (Enter your answers as a comma-separated list. Enter all answers including repetitions.)
(b) Factor P completely.
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Q2: A polynomial P is given.
P(x) = x^4 − 256
a) Find all zeros of P, real and complex. (Enter your answers as a comma-separated list. Enter all answers including repetitions.)
b) Factor P completely.
Answers
Answered by
oobleck
x^5 + 4x^3
= x^3 (x^2+4)
= x^3 (x+2i)(x-2i)
x^4 - 256
= (x^2-16)(x^2+16)
= (x-4)(x+4)(x-4i)(x+4i)
= x^3 (x^2+4)
= x^3 (x+2i)(x-2i)
x^4 - 256
= (x^2-16)(x^2+16)
= (x-4)(x+4)(x-4i)(x+4i)
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