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Home > INT3 > Chapter 8 > Lesson 8.3.2 > Problem 8-120

8-120.

Spud has done it again. He has lost another polynomial function. This one is 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? Homework Help ✎

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))
x2 + 4x + 29

Multiply the result by (x + 1).

(x + 1)(x2 + 4x + 29)

p(x) = x3 + 5x2 + 33x + 29