Answer
(a) Fill the blank with $(x-a)$
(b) Fill the blank with $(x-a)^{m}$
Work Step by Step
Complete Factorization Theorem (p.287)
$P$ factors into $n$ linear factors : $P(x)=a(x-c_{1})(x-c_{2})\cdots(x-c_{n})$
where $a$ is the leading coefficient of $P$ and $c_{1}, c_{1}, \ldots, c_{n}$ are the zeros of $P$.
(a) Fill the blank with $(x-a)$
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Zeros Theorem (p.289)
Every polynomial of degree n $\geq$ 1 has exactly n zeros, provided that a zero of multiplicity k is counted k times.
(b) Fill the blank with $(x-a)^{m}$
