Question

A polynomial f(x) with real coefficients and leading coefficient 1 has zeros 7 + 8i, -9 + i and degree 4. Express f(x) as a product of quadratic polynomials with real coefficients that are irreducible over IR.

Answer 1

\[x = 7 + 8i\]
\[(x - 7)^2 = -64\]
\[ x ^{2} - 14x + 113 = 0 = P(x)\]

Answer 2

\[x = -9 + i\]
\[x ^{2} + 18x + 82 = o = Q(x)\]

Answer 3

R(x) = P(x) Q(x)

Answer 4

Super, thanks!