Form a polynomial f(x) when the degree is 5 and the zeros are 2, -i, i, 1-i, 1+i
+37167 (x-2)(x+i)(x-i)(x -1+i)(x-1-i) = polynomial
multiply all of this out to get:
x5 - 4x4 + 7x3 - 8x2 +6x -4
+15069 Form a polynomial f(x) when the degree is 5 and the zeros are 2, -i, i, 1-i, 1+i
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f(x)=(x+i)(x−i)(x−1+i)(x−1−i)(x−2)=(x2+1)(x−2)(x2−x−ix−x+1+i+ix−i+1)=(x2+1)(x−2)(x2−2x+2)=(x2+1)(x3−2x2+2x−2x2+4x−4)=(x2+1)(x3−4x2+6x−4)
=x5−4x4+6x3−4x2+x3−4x2+6x−4=x5−4x4+7x3−8x2+6x−4
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