Answer
True
Work Step by Step
By the corollary to the fundamental theorem of algebra, a polynomial of degree n with real coefficients
has exactly n complex roots, counting the multiplicity of each root.
1. If c is a real root of the polynomial P(x), then (x-c) is a ${\bf \text{ linear}}$ factor of P(x).
2. If c is a complex root, $c=a+bi$, then its conjugate $\overline{c}=a-bi$ is also a root of P.
Both $(x-c)$ and $(x- \overline{c})$ are factors of P:
$(x-a-bi)(x-a+bi)=(x-a)^{2}-(bi)^{2}$
$=x^{2}-2ax+a^{2}+b^{2}$,
which is a ${\bf \text{quadratic (irreducible)}} $factor of P.
The statement is true.