How do you write a polynomial in standard form given the zeros 1 and 4-4i?

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Answer 1 · 2017-03-10T07:25:12

#x^3 -9 x^2 +40x - 32#

Complex zeros always come in pairs: #4 +-4i#

Always multiply the complex zeros first to get rid of the complex terms by remembering that #i^2 = -1#

Multiply the complex factors: #(x-4-4i)(x-4+4i)#

#= x^2 -4x + 4ix -4x +16 -16i -4ix +16i -16i^2#

Simplify by adding like terms:
#= x^2 - 8x + 16 -16(-1)#
#= x^2 - 8x + 32#

Add the #(x-1)#, #(x=1)# factor to the equation:

#(x-1)(x^2 - 8x + 32)#

Multiply using distribution:
#x^3 - 8x^2 +32x -x^2 +8x - 32#

Simplify by adding like terms:
#x^3 -9 x^2 +40x - 32#