# Thread: find r .... exponents

1. ## find r .... exponents

I can't figure out the right approach...

put in a screen shot because I'm not sure about notation on the forum

Thanks!

2. This is a long division problem (you'll also find a,b and c as a bonus). In this case r will be your final remainder

Since it's a nightmare to do on latex I'll link to Wolfram: http://www.wolframalpha.com/input/?i...29%2F%28x-4%29

3. $\displaystyle \frac{3x^3-2x^2+2x-2}{x-4} = ax^2+bx+c+\frac{r}{x-4}$

$\displaystyle \Rightarrow 3x^3-2x^2+2x-2 = (x-4)(ax^2+bx+c)+r$

$\displaystyle \Rightarrow 3x^3-2x^2+2x-2 = ax^3+(b-4a)x^2+(c-4b)x-4c+r$

Comparing the coefficients:

It's obvious that $a = 3$.

Therefore $b-4a = -2 \Rightarrow b = 10$.

So $c-4b = 2 \Rightarrow c = 42$.

Finally $-4c+r = -2 \Rightarrow r = 166.$