Question

PLS pls pls help
The polynomial P(x) is divided by (x-1)(x+2). Find the remainder if, given that P(1)=2 and P(-2)= 5

Answer 1

@satellite73 help pls pls pls. I been stuck on this one for days...

Answer 2

do you recall the remainder thrm?

Answer 3

yea
P(x) = (x-1)(x+2) Q(x) + R

Answer 4

Since the P(1) and P(-2) are not zero, we know that the given is not a divisor right?

Answer 5

ye

Answer 6

what ideas have you run thru so far?

Answer 7

i tried to sub P(1) and P(-2) into (x-1)(x+2) Q(x) + R

Answer 8

yeah, all that really tells us is that R = 1 or -2 :)

Answer 9

we are given 2 points, the least poly to fit between 2 points is a line, right?

Answer 10

oh yea...

Answer 11

and since the given is an x^2, the top would have to be the remainder ... of at most x

Answer 12

you get where this is going?

Answer 13

kinda...

Answer 14

\[\frac{P(x)}{(x-1)(x+2)}=Q(x)+\frac{R(x)}{(x-1)(x+2)}\]

Answer 15

R(x) is a poly of at most, degree 1; and since its value changes, it cant be a constant and must be a line

Answer 16

the line between 1,2 and -2,5

Answer 17

oh....

Answer 18

im assuming you know how to define that line ...

Answer 19

with gradient -1 right?

Answer 20

maybe, i hadnt quite gotten to the line :)

Answer 21

then i got line 3-x

Answer 22

thats a great line

Answer 23

would that really be the answer?

Answer 24

and any multiple of it would work as well

Answer 25

\[R(x)=k(3-x)\]

Answer 26

the k migh tbe a little much tho; 3-x is sufficient

Answer 27

yea thanks so much!!!

Answer 28

youre welcome

Answer 29

you're* LOLOLOL

Answer 30

.... they dont put that key in an opportune spot ;)