## anonymous 5 years ago Use long division to perform the division (Express your answer as quotient + remainder/divisor.)

1. anonymous

$x^4+8x^3-4x^2+x-2 \over x-2$

2. anonymous

do you know how to use 'synthetic division'? i can try to write it if you do not

3. anonymous

i am no good with division at all

4. anonymous

oh actually it says "long division" doesn't it. ok then take out paper and pencil and write like you would a regular long division problem $x-2|x^4+8x^3-4x^2+x-2$

5. anonymous

something like that. or would you just like to use synthetic division it is much much easier.

6. anonymous

i believe it wants me to work it out the way you wrote it up top

7. anonymous

list the coefficients of the numerator 1 8 -4 1 -2

8. anonymous

ok they we are in for a world of annoyance. fine, write what i did first. now forget about the -4 for a moment. what is $x^4$ divided by $x$?

9. anonymous

in other words how many times does $x$ go in to $x^4$ or even more simply what is $\frac{x^4}{x}$?

10. anonymous

1?

11. anonymous

no, try this. what is $\frac{2^4}{2}$?

12. anonymous

8

13. anonymous

yes, aka $2^3$

14. anonymous

what do you think $\frac{5^4}{5}$ is without computing

15. anonymous

what do you mean without computing?

16. anonymous

i mean write your answer as 5 to a power

17. anonymous

not sure i follow...

18. anonymous

ok lets try this $\frac{x^4}{x}=\frac{x\times x \times x\times x}{x}$ and when you cancel one of the x's what do you get?

19. anonymous

you should get x to a power yes?

20. anonymous

Or you can think of it as "What do I need to multiply times x to get $$x^4$$"

21. anonymous

polpak you get the award for the day with $b^0$!

22. anonymous

=)

23. anonymous

now lets see if we (you) can help mathater realize that $\frac{x^4}{x}=x^?$

24. anonymous

because we have a long division to do.

25. anonymous

I don't think it'll work cause they're not here anymore ;)

26. anonymous

yes, the problem is variables are confusing if you are not used to them. that is why $\frac{x^4}{x}=1$ cancel the x's and $1^4=1$!