Question

When the polynomial mx^3-3x^2+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. -- How would i do this question, i know how to do it with one unknown variable but not 2.

Answer 1

well, you have two unknowns, therefore two equations

first, x+3 means x=-3
sub that into the polynomial
equate that to the remainder, which is -1

then x-2 means x=2
sub that into the polynomial too
equate that to the remainder, which is -4

then use simultaneous equations to solve for the two unknowns

Answer 2

Yes I understand that part but I don't know how to get value of the unknown variables when 2 are unknown.

Answer 3

you don't know how to simultaneously solve equations?

first, when you have two equations with similar terms
make one of them the subject for both
so say you choose m, make both equations into something like
m=_____________
m=_____________

then equate them to each other, and you'll find n
using the value of n, find m

Answer 4

I'm still confused, how would I get the unknown m when the n is still unknown. Wouldn't I get something like m=3n (just an example)

Answer 5

try the steps out and you'll see

the concept is that when you equate lets say, y=3m and y=5+2m
you'll get 3m=5+2m, which is an equation with only one unknown

after i solve for that,
3m=5+2m
3m-2m=5
m=5

i just plug it back into the original equation to find y
you can choose either one, i'll go for y=3m
y=3m
y=3(5)
y=15

there, you've got both unknowns

Answer 6

I get it, thanks.