Question

What is the remainder when (2x^4−4x^2−16) is divided by (x+2)

Answer 1

Okay, have you learned either long division for polynomials or synthetic division yet?

Answer 2

prolly but i dont really pay attention

Answer 3

Ok
So, which one do you want to use, long division or synthetic division
(synthetic division is shorter, easier after youget how to do it

Answer 4

synthetic ig

Answer 5

Okay
so we have to set it up
For synthetic division, we divide it be (x-_), which means that because int his we are dividing by x+2, we have to use -2

Answer 6

Also, we only write down the coefficients for these

Answer 7

And because we don't have x^3 or x, we fill it in as a 0

Answer 8

ok

Answer 9

it looks confusing, but each of the numbers are actually just coefficients

Answer 10

ok

Answer 11

And so, we drop down each one, multiply it by -2, but it to above the line, etc., i'll show you

Answer 12

multiply 2 and -2

Answer 13

different than long division, synthetic division does addition

Answer 14

multiply -2 and -4

Answer 15

add -4 and 8

Answer 16

multiply -2 and 4

Answer 17

add 0 with -8

Answer 18

mutliply

Answer 19

And so, we are left with 0 at the end
if at the end you do not get 0 for once, that means that that is the remainder

Answer 20

So, filling in the gaps again with those x's
you get
2x^3 + -4x^2 +4x-8

Answer 21

do i just solve it from there?

Answer 22

._.
that's your answer

Answer 23

oh im stupid i swear lol

Answer 24

What we just did was divide
you didn't get any of it?
oof

Answer 25

the answers im given on the question are -16, -8, 0, and 8

Answer 26

\(\color{#0cbb34}{\text{Originally Posted by}}\) @snowflake0531
And so, we are left with 0 at the end
if at the end you do not get 0 for once, that means that that is the remainder
\(\color{#0cbb34}{\text{End of Quote}}\)

Answer 27

Which means that it is 0

Answer 28

ohh

Answer 29

The division was perfect, there's no remainder

Answer 30

oka i get it

Answer 31

yw~

Answer 32

thanks!

Answer 33

yw~, it was fun