Question

If f(x)= 5x^5+1, then what is the remainder when f(x) is divided by x+1?

Answer 1

@jhonyy9

Answer 2

Divide:5/6 ÷ 1/4

20/6
3 1/3
5/24
10/3

Answer 3

I don't get it

Answer 4

ok so I'd do synthetic division for this.
so first you have to make sure it's in standard form and see if you need any place holders. In this case you do because we have an exponent of 5 and then we go right to a constant.
you can rewrite this as
\[\frac{ 5x^5 +0x^4+0x^3+0x^3+0x^2+0x+1}{ x+1 }\]
this will help when you do the actual division.
make sense so far?

Answer 5

Yeah

Answer 6

remainder theorem

Answer 7

f(-1) = ??

Answer 8

ok so then we need set x+1 equal to zero.
\[x+1=0\]
then we subtract 1 from both sides, and get x=-1.
now we can start dividing. so you set it up as:

so do you know how to do synthetic division?

Answer 9

No

Answer 10

ok so you see what i did up there? ^
you are going the drop the 5 down:

then what is -1*5?

Answer 11

-5

Answer 12

yes, so you write that under the 0.

then you add: 0+ (-5) = ?

Answer 13

-5

Answer 14

\(\color{#0cbb34}{\text{Originally Posted by}}\) @mxddi3
yes so you would bring that down the same way you did with the first 5.
then you repeat.
what is -1*(-5)?
take that answer and write it under the next 0.
keep going until the end.
the last number will be your remainder.
do you got it or do you need me to show it to you?
\(\color{#0cbb34}{\text{End of Quote}}\)

Answer 15

Show me please

Answer 16

ok you -1*(-5)=5 so you would write 5 under the next 0. then you repeat. 0+5=5, so you bring down the five. -1*(5)= -5 so you write that under the next zero.
you keep going until you get to the end, and you will have 1-5=?
this is your remainder.
does this make any type of sense?

Answer 17

5

Answer 18

go to the very end.
i did all the 5's and -5's for you.
now you need to see what is 1-5?

Answer 19

4

Answer 20

close.
5 is larger than one, so it wouldn't be positive 4.
if i have one dollar but i have to give you 5, im going to OWE you 4 which means i'd be at -4

Answer 21

Oh my bad my brain decided to stop

Answer 22

I knew that

Answer 23

it's cool, lmao.
does the overall process make sense?

Answer 24

Yeah

Answer 25

Damn maddie smarter than i thought Nice job maddie

Answer 26

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