SATMathematics Practice Test 1

If the polynomial p(x) is divided by $\mathit{x}-3$,
the result can be written as $\frac{\mathit{p}\left(\mathit{x}\right)}{\mathit{x}-3}=\mathit{q}\left(\mathit{x}\right)+\frac{\mathit{r}}{\mathit{x}-3}$.
where $\mathit{q}\left(\mathit{x}\right)$ is a polynomial and r is the remainder.
Since x − 3 is a degree 1 polynomial, the remainder is a real number. Hence, $\mathit{p}\left(\mathit{x}\right)$ can be written as $\mathit{p}\left(\mathit{x}\right)=\left(\mathit{x}-3\right)\mathit{q}\left(\mathit{x}\right)+\mathit{r}$, where r is real number.
It is given that $\mathit{p}\left(3\right)=-2$ so it must be true that .
Therefore, the remainder when p(x) is divided by $\mathit{x}-3$ is $-2$
Choice A is incorrect because p(3) = −2 does not imply that p(5) = 0.
Choices B and C are incorrect because the remainder −2 or its negative, 2,need not be a root of p(x).