## burhan101 3 years ago When polynomial mx³-3x²+nx+2 is divided by x+3, the remainder is -1. When it is divided by x-2, the remainder is -4. Determine the values of 'm' and 'n'.

1. helder_edwin

use synthetic division

2. lgbasallote

are you familiar with the remainder theorem?

3. helder_edwin

that's better. sorry

4. burhan101

|dw:1347327495204:dw|

5. burhan101

and yes i am familiar with the remainder theorem, am i doing this right so far ?

6. lgbasallote

yup

7. lgbasallote

now...just add 1 to both sides...to get something fun

8. burhan101

|dw:1347327616779:dw|

9. lgbasallote

right to..add 4 to both sides there

10. lgbasallote

too*

11. burhan101

|dw:1347327802473:dw|

12. burhan101

now i dont know what to do next

13. lgbasallote

yes. now simplify those

14. lgbasallote

-27m -3n - 24 = 0 everything is divisible by 3

15. lgbasallote

8m + 2n - 6 = 0 everything is divisible by 2

16. burhan101

|dw:1347327965579:dw|

17. burhan101

like that ?

18. burhan101

or with the coeff

19. lgbasallote

right

20. lgbasallote

-9m - n - 8 = 0 4m + n - 3 = 0 now you can do system of linear eqn

21. burhan101

i can let is equal any number right ?

22. lgbasallote

yes. you can also do elimination

23. burhan101

let m=1 -9(1)-n-8=0 -9-n-8=0 -n=9+8 n=17 subst. n=17 in 2nd equation 4m+17-3=0 4m+14=0 m= -7/2

24. lgbasallote

that's an unorthodox method...

25. lgbasallote

where did you learn that?

26. burhan101

i dont know, i think im confusing it with something else

27. lgbasallote

it's the plotting of points method...it doesn't work here lol

28. burhan101

oh woops !

29. lgbasallote

anyway... -9m - n - 8 = 0 4m + n - 3 = 0 try adding the equations...what do you get?

30. burhan101

m= -11/5

31. burhan101

and now subst

32. lgbasallote

right

33. burhan101

n=29/5

34. lgbasallote

right. so there you go

35. burhan101

thank you so much ! :)

36. lgbasallote

welcome