SOLUTION: Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. 7, -11, and 2 + 8i I understand

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Question 1079506: Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form.
7, -11, and 2 + 8i
I understand that I have to foil these and that I have to find the conjugate, however, I am struggling with how to FOIL (x-(2+8i))(x-(2-8i))

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
given zeros:
x%5B1%5D=7,x%5B2%5D=+-11, and x%5B3%5D=2+%2B+8i
since given x%5B3%5D=2+%2B+8i, we will have x%5B4%5D=2-+8i too because complex zeros always coming in pairs
using zero product formula, we have
f%28x%29=%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29%28x-x%5B4%5D%29
f%28x%29=%28x-7%29%28x-%28-11%29%29%28x-%282+%2B+8i%29%29%28x-%282-+8i%29%29
f%28x%29=%28x-7%29%28x%2B11%29%28x-2+-+8i%29%28x-2%2B+8i%29

f%28x%29=%28x%5E2+%2B+4x+-77%29%28x%5E2-4x%2B4-64%28-1%29%29
f%28x%29=%28x%5E2+%2B+4x+-77%29%28x%5E2-4x%2B4%2B64%29
f%28x%29=%28x%5E2+%2B+4x+-77%29%28x%5E2-4x%2B68%29
f%28x%29=x%5E4+-+25x%5E2+%2B+580x+-5236