Question

(2x^(4)-x^(3)+1)/(x+3) Use remainder theorem to find the remainder.
Please show all work.
Thanks.

Answer 1

the remainder thrm just says that there is an added remaineder to the answer ;)

Answer 2

P(x) = Q(x) + R(x)

Answer 3

we divide these like they were any other numbers.... division is division regardless of what you divide..

Answer 4

the key is to remember how long division is done; or use synthetic division

Answer 5

i have to use long division but im confused because in order to devide i have to 2x^4 times (x+3) then it would be 2x^4 -x^3 over 2x^4- 6x^3 and then i got confused

Answer 6

we can work thru that are you remembering to subtract your answers?

Answer 7

what do you mean exactly u mean 2x^4- 2x^4 = 0 and then -x^3 - (-6x^3)?

Answer 8

2x^3 <- 2x^3(x+3)= (2x^4+6x^3), but we subtract this result
---------------- to get our next round......
x+3| 2x^4 -x^3 +1
-2x^4 -6x^3
------------
-7x^3 +1

Answer 9

remember how to do it with numbers? same thing:

3 <- 6(3) = 18....what do we do with the 18?
-----
6| 19
-18 <- we subtract it....
-------
1

Answer 10

ok i see where i messed up originally now we times (x+3) by 7x^2? and then work the problem?

Answer 11

2x^3 -7x^2
----------------
x+3| 2x^4 -x^3 +1
-2x^4 -6x^3
------------
-7x^3 +1
+7x^3 +21x^2
---------------
21x^2 +1 <- whatever doesnt cancel out gets brought down

Answer 12

not (x+3) times 21x?

Answer 13

the next number need to be the same as this bottom first number...or at least get to equal it.... we need a 21; and x*x=x^2 so....... 21x

Answer 14

thats right ;)

Answer 15

wait never mind it needs to be by -21x^2?

Answer 16

2x^3 -7x^2 +21x
----------------
x+3| 2x^4 -x^3 +1
-2x^4 -6x^3
------------
-7x^3 +1
+7x^3 +21x^2
---------------
21x^2 +1
-21x^2 -63x
-------------
-63x +1

Answer 17

do you understand that we are subtracting the result?

Answer 18

now just (x+3) times 63?
and yes sir/ma'am

Answer 19

x times ??? = -63x ?

Answer 20

63 right so we get 63x+189?

Answer 21

and then remainder is 190?

Answer 22

thats right :)

now...

-63x - (63x) = 0 right?

Answer 23

Yeah.

Answer 24

2x^3 -7x^2 +21x -63x
----------------
x+3| 2x^4 -x^3 +1
-2x^4 -6x^3
------------
-7x^3 +1
+7x^3 +21x^2
---------------
21x^2 +1
-21x^2 -63x
-------------
-63x +1
+63x +189
-------------
190 <- remainder :)

Answer 25

Thanks!

Answer 26

synthetic is similar, but we already work with an opposite so we add stuff....

(x+3)..x=-3

-3|2 -1 0 0 1
0 -6 21 -63 189
-------------------
2 -7 +21 -63 190 <- remainer 190
^^^^^^^^^^^
2x^3 -7x^2 +21x -63