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

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 ± 5*i* and one real zero, −1. What could his original function have been? Homework Help ✎

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

*p*(*x*) = (*x* − (− 1))(*x* − (−2 + 5*i*))(*x* − (−2 − 5*i*))

Multiply the two complex polynomials.

(*x* − (−2 + 5*i*))(*x* − (−2 − 5*i*))*x*^{2} + 4*x* + 29

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

(*x* + 1)(*x*^{2} + 4*x* + 29)

*p*(*x*) = *x*^{3} + 5*x*^{2} + 33*x* + 29