Question

PRECALCULUS HELP !
help me understand remainder theorem

Answer 1

my notes has :

The Remainder Theorems

The Remainder Theorem states:
If a polynomial f(x) is divided by (x – k), the remainder is r = f(k).
This means we can find a point on the graph of a function by choosing a value k for x = k and using division to get a remainder. The remainder will be the y coordinate of the point on the graph.

For example:
For x = 2 and f(x) = x4 + 2x3 – 4x2 + x - 6, we determined in the previous Test your skills exercise that the remainder was 12. Therefore, there is a point (2, 12) on the graph of the function.

Answer 2

If \(f(x)\) is divided by \(x - k\), then the remainder is \(f(k)\).

Answer 3

why the remainder gives y coordinate ?

Answer 4

yes, why/how... i dont see it

Answer 5

a numerical example or something would help...

Answer 6

Because \(f(2) = 12\), there is a point \((2,12)\) on the graph. Not to think too hard about it!

Answer 7

yay i see !!!!!!! thank you :) thats perfect and to the point explanation ! thnks a lot :)

Answer 8

You're welcome!

Answer 9

since f(2) = 12,
if we divide f(x) by (x-2), we get a remainder of 12 !

Answer 10

Yeah, and I know how to derive it, if you want to know...

Answer 11

i would like to go through if u have time and if its easy

Answer 12

\[\text{Dividend = Divisor}\rm \cdot Quotient + Remainder\]Now let's say that the dividend is \(f(x)\), the divisor is \(x - k\), the quotient is \(q\) and remainder is \(R\).\[f(x) = (x - k)\cdot q + R\]What if we substitute \(x\) with \(k\) in the equation?\[f(k) = q(x - x) + R\]\[f(k) = 0q +R\]\[f(k) = R\]

Answer 13

It's really easy, actually!

Answer 14

if R= 0, then (x-k) is a factor of f(x).


yesssssssssssssssss its easy now after your explanation ! ty so soo much xD

Answer 15

And that's the factor theorem you were talking about. :)

Answer 16

lol thats coming up next... ;)

Answer 17

when only some right person explains me i learn very fast than on my own :| ima bug u with more tomorrow cya ;P

Answer 18

lol