Chapter 3, Polynomial and Rational Functions - Section 3.5 - Complex Zeros and the Fundamental Theorem of Algebra - 3.5 Exercises - Page 329: 6

a. False b. True c. False

$P(x)=x^3+x$, $P(x)=x(x^2+1)=0$ $x=0$ or $x^2+1=0 x=\pm \sqrt {-1}, x=\pm i$. Thus, a. False, the polynomial has only one real zero. b. True, $0$ is the only real zero of the polynomial. c. False, $P(x)=x(x^2+1)$ can be factored into linear factors and irreducible quadratic factors, not only linear factors.