The science fair judges will be teachers and volunteers. Each judge will view 5 projects. There are 133 science teachers. What i
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Since , by the remainder theorem this means that <em>x</em> - 6 divides <em>f(x)</em> exactly. This means there are constants <em>a</em>, <em>b</em>, and <em>c</em> such that
Multiplying both sides by <em>x</em> - 6 gives
Then <em>a</em>, <em>b</em>, <em>c</em> satisfy
and solving this system gives <em>a</em> = 2, <em>b</em> = -7, and <em>c</em> = 3.
So, we have
The quadratic term can be factored as
which leaves us with
so that the zeros of <em>f(x)</em> are 6, 1/2, and 3.