posted by gabs .
A polynomial f(x) with real coefficients and leading coefficient 1 has zeros 6 + 4i, -5 + i and degree 4. Express f(x) as a product of quadratic polynomials with real coefficients that are irreducible over R.
ive done this problem every which way i could. specifically i understand that imaginary numbers come in pairs so i wrote: 6+4i, 6-4i, -5+i, -5-i and i put all thos equal to x, subtracted the x so the equation is equal to zero and then began to multipy them .
can someone please write out the steps for me and then give me the format this answer is supposed to be in..PLEASE HELP!
(x-6+4i)(x-6-4i)(x+5+i)(x+5-i) = 0
(x^2 -12 x + 52)(x^2 + 25 x + 26)
x^4 +13 x^3 -222 x^2 + 988 x +1352