1. Consider the polynomial [math]f\left(x\right)=x^2-5x+2[/math]. Let [math]r_1\left(x\right)[/math] be the remainder when we divide [math]f\left(x\right)[/math] by [math]\left(x-1\right)[/math]. That is, [math]r_1\left(x\right)[/math] satisfies [math]\frac{f\left(x\right)}{x-1}=q\left(x\right)+\frac{r_1\left(x\right)}{x-1}[/math] where the degree of [math]r_1\left(x\right)[/math] is less than the degree of the divisor, [math]\left(x-1\right)[/math] . Find and graph [math]r_1\left(x\right)[/math] on the set of axes below.
2. Now, find the remainder [math]r_2\left(x\right)[/math] that results from dividing [math]f\left(x\right)[/math] by [math]\left(x-1\right)\left(x-1\right)[/math]. Graph [math]r_2\left(x\right)[/math] on the set of axes below.
3. What do you notice about each remainder at the point P?
4. What do you think the remainder graph would have looked like if we considered [math]\frac{f\left(x\right)}{x^2-4x+4}[/math]?