SOLUTION: A polynomial f(x) with real coefficients and leading coefficient 1 has the given zeros and degree. Express f(x) as a product of linear and/or quadratic polynomials with real coeffi

Algebra ->  Inequalities -> SOLUTION: A polynomial f(x) with real coefficients and leading coefficient 1 has the given zeros and degree. Express f(x) as a product of linear and/or quadratic polynomials with real coeffi      Log On


   

Question 1171424: A polynomial f(x) with real coefficients and leading coefficient 1 has the given zeros and degree. Express f(x) as a product of linear and/or quadratic polynomials with real coefficients that are irreducible over ℝ.
1, −5 − 4i; degree 3
Answer by CubeyThePenguin(3113) About Me  (Show Source):
You can put this solution on YOUR website!
If a polynomial has the root a + bi, it also has the root a - bi.

Here, a is a constant.

a(x - 1)(x - (-5 - 4i))(x - (-5 + 4i))
a(x - 1)(x^2 + 10x + 41)
a(x^3 + 9x^2 + 31x - 41)