### Home > CCA2 > Chapter 8 > Lesson 8.3.2 > Problem8-147

8-147.

Spud has done it again. He's lost another polynomial function. This one was a cubic, written in standard form. He knows that there were two complex zeros, $-2 ± 5i$ and one real zero, $-1$. What could his original function have been?

Use the three zeros to write the polynomial in factored form.

$p(x) = (x - (- 1))(x - (-2 + 5i))(x - (-2 - 5i))$

Multiply the two complex polynomials.

$(x - (-2 + 5i))(x - (-2 - 5i))$
$x^2 + 4x + 29$

Multiply the result by $(x + 1)$.

$(x + 1)(x^2 + 4x + 29)$

$p(x) = x^3 + 5x^2 + 33x + 29$