Question

A student divided f(x)=3x^3+8x^2+5x-4 by x+2 and found the remainder was r=-6. based on the remainder theorem, what can be concluded about f(x)?

Answer 1

well since the remainder wasn't 0 you can conclude that x+2 is not a ______

Answer 2

think f word

Answer 3

For example the remainder when (x^2-x) is divided by x is 0
but x^2-x can be written as x(x-1)
What is x and x-1 called of x^2-x?

Answer 4

idk

Answer 5

Can you complete this sentence:
3 is a _______ of 9

Answer 6

What if I asked you to factor 9? OR write the factors of 9?

Answer 7

3 times 3

Answer 8

ok the factors of (x^2-x) are x and x-1
so dividing (x^2-x) by either one its factors will give you a remainder of 0
just like if you divide 9 by one of its factors you get a remainder of 0

Answer 9

so when we have f(x) divided by d(x) giving us a remainder of 0
then that tells us that d(x) is a __________ of f(x)

Answer 10

and when we don't get a remainder 0 then d(x) is not a __________ of f(x).

Answer 11

it is hard not to get this one since I told you the first letter of the word
and I repeated the word a few times

Answer 12

ok I know it's factor. there are 4 choices:
a) the point (-2,-6) lies on the graph of f(x)
b) the function f(x)3x^3+8x^2+5x-4 has a zero at -6
c) the y-intercept of the graph of f(x)=-6
d) the function f9x)3x^3+8x^2+5x-4 has a zero at -2

Answer 13

oh no that isn't what I was trying to get you to see
i was trying to get you to see it isn't a factor

Answer 14

the remainder is not 0 so it (x+2) is not a factor
if the remainder was 0 (x+2) is a factor

Answer 15

well you can find the remainder of f(x) divide by (x+2) by simply plugging in -2 into the original function

Answer 16

ok, yes, I know that. which one do you think is the answer out of the 4 I just gave?

Answer 17

So if I tell you f(-2)=remainder=-6 in this case
then what could you tell me

Answer 18

For example pretend f(x)=x^2-x
dividing it by x-4 gives a remainder of 12
Well that would mean f(4)=12 by remainder theorem

Answer 19

f(x)=y tells a point on f
that point being (x,y)

Answer 20

so if have f(4)=12 that means (4,12) on a point on f(x)=x^2-x

Answer 21

do you understand what the answer is yet?

Answer 22

yes, I got it. thank you for your time