Question

Use the remainder theorem to find the value for each when:
f(x) = x^4 + 3x^2 + 5
g(x) = x^3 -3x^2 +x -7

f(2)=
f(-3)=
g(3)=
f(4)=

Answer 1

To find f(2) using remainder theorem, divide f(x) by (x-2) either by synthetic or long division and find the remainder. That remainder will be the value of f(2).

Answer 2

i don't understand how to do the theorem or this would be easier to understand @ranga

Answer 3

Divide x^4 + 3x^2 + 5 by (x - 2) and tell me the remainder you get.

Do you know synthetic division?

Answer 4

-2 would be x^4 right? and yes i do

Answer 5

There are some missing exponents in x^4 + 3x^2 + 5. So write it as:
x^4 + 0x^3 + 3x^2 + 0x + 5. Then do synthetic division:
|
-2 | 1 0 3 0 5
|
|__________________________

Answer 6

0 replaces the x right?

Answer 7

0 in the place of missing x^3 and missing x

Answer 8

i would then add all of them right?

Answer 9

In synthetic division, you will drop the 1 first, multiply it by -2 put it under 0, add, etc..

Answer 10

so i would add -2 to 0, then drop the 3 multiply it by -2 drop it under the zero to get -6 and then multiply 5 times -2 to get -10, add all of them to get -18??

Answer 11

@ranga

Answer 12

You may want to watch a couple of videos on synthetic division first. Here is one: http://www.youtube.com/watch?v=bZoMz1Cy1T4

Answer 13

okay i will really quick!

Answer 14

It should have been a 2 (not a negative 2) on the left:

|
2 | 1 0 3 0 5
|
|__________________________

Answer 15

so what i was doing was kinda on the right track

Answer 16

yeah. but you don't drop the 3. You multiply the previous digit, put it under 3, add, etc.

Answer 17

The first 1 is the one you drop directly. For the rest multiply, put it under the next column, add, then multiply, put it in the next column, etc.

Answer 18

1 2 7 14 24??

Answer 19

wait 47 would be the end number

Answer 20

1,2,7,14 are good. But 24 is not.

Answer 21

it would be 47

Answer 22

No. Up to 14 is good. Multiply 14 by 2 put it under 5 and add.

Answer 23

14*2= 28 28+5=33 whoops

Answer 24

Yes. That 33 that you found is the same as what you will get if you
put x = 2 in x^4 + 3x^2 + 5

Answer 25

so f(-3) would equal 113

Answer 26

Yes. But for this problem they want you to find it the roundabout way of doing synthetic division by -3 and finding the remainder. I guess they want you to get good at synthetic division.

Answer 27

i can understand that, so f(4) would equal 309
would the set of for g(3) be 3l 1 -3 1 -7

Answer 28

f(4) = 309 is correct.
Yes that will be the synthetic division you need to perform for g(3).

Answer 29

it turned out to be 50 but 50 is not a option

Answer 30

Some mistake in synthetic division somewhere. Watch another video on YouTube. Type in synthetic division and you will get a bunch of videos.

Answer 31

but i thought i did it right because 3 l 1 -3 1 -7
drop it would be 3 6 19 50

Answer 32

3 time 1 is 3, 3 times 3 is 9 + -3 is 6, 6 times 3 is 18 plus 1 is 19, 19 times 3 is 57 + -7 equals 50

Answer 33

|
3 | 1 -3 1 -7
| 3 0 3
|______________________________
1 0 1 -4

Answer 34

whoops i multiplied!

Answer 35

And you can always check your answer by putting x = 3 in g(x) and verifying if it is -4.

Answer 36

it is! thank you so much! I may need help again would you be willing to help?

Answer 37

If I am around I will but I may not be for a while. Other work is piling up. :)
You are welcome.