Answer:
[tex]\dfrac{17x^3-221x^2+425x-5525}{9}\\[/tex]
Step-by-step explanation:
hello
we need to find something like, a being real
[tex]a(x-13)(x-5i)(x+5i)[/tex]
with a so that
[tex]a(3-13)(3-5i)(3+5i)=-680\\\\<=>a(-10)(3^2-(5i)^2)= -10(9+25)a=-360a=-680\\<=> a = \dfrac{680}{360}=\dfrac{17*40}{9*40}=\dfrac{17}{9}[/tex]
so the third degree polynomial that we are looking for is
[tex]\dfrac{17}{9}(x-13)(x-5i)(x+5i)\\=\dfrac{17}{9}(x-13)(x^2+25)\\\\=\dfrac{17}{9}(x^3+25x-13x^2-13*25)\\\\\\=\dfrac{17}{9}(x^3-13x^2+25x-325)\\\\\\\\=\dfrac{17}{9}x^3-\dfrac{17*13}{9}x^2+\dfrac{17*25}{9}x-\dfrac{17*325}{9}\\=\dfrac{17}{9}x^3-\dfrac{221}{9}x^2+\dfrac{425}{9}x-\dfrac{5525}{9}\\[/tex]
hope this helps
