Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. 4, -14, and 5 + 8i

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Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. 4, -14, and 5 + 8i

Mathematics
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If 5 + 8i is a zero, then 5 - 8i must also be a zero. Now combine the zeros and multiply \[f(x)=(x-4)(x+14)(x-5+8i)(x-5-8i)\]
f(x)=(x−4)(x+14)(x−5+8i)(x−5−8i)

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Other answers:

x^4-9x^3
how would i do the rest
id either get 725x or 1450x
I'm not sure how you got x^4-9x^3. You need to multipliy these using the distributive property. Start with (x−5+8i)(x−5−8i) to eliminate the imaginary parts
x^2-5x-8ix-5x+25+40i+8ix-40i
you're missing -64i², which simplifies to 64. Now combine like terms. All the parts with i will cancel out
x^2-10x+25-64i^2+81x
there's no 81x. Just \(x^2-10x+25-64i^2\) and -64i² = 64. So once you combine it's \[x^2-10x+89\]
Set that off to the side and multiply (x-4)(x+14)
x^2+14x-4x-56 x^2+10x-56
Right :) so now all that's left is to multiply the two quadratics \[(x^2-10x+89)(x^2+10x-56)\]
(x2−10x+89)(x2+10x−56) x^4+10x^3-56x^2-10x^2+560+89X^2+890x-4989
x^4+10x^3+23x+890x-4429
you missed a term (-10x)(10x) and 89*56 = 4984. Altogether it should be \[x^4+10x^3-56x^2-10x^3-100x^2+560x+89x^2+890x-4984\]
x^4+67x^2+1450x-4984
C thank you!
\[x^4-67x^2+1450x-4984\] yes C

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