Answer
(a) false
(b) true
(c) false
Work Step by Step
Linear and Quadratic Factors Theorem (p. 292)
Every polynomial with real coefficients can be factored into linear and irreducible quadratic factors with real coefficients.$- $
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$P(x)=x^{3}+x=x(x^{2}+1)$
The second factor does not have real zeros, $x^{2}+1=(x+i)(x-i)$
$P$ has one real zero and two complex zeros.( $0$ and $\pm i$ )
$P(x)=x(x+i)(x-i)$
(a) false
(b) true
(c) false, the factors are: one linear and one quadratic.
