Question

Find the remainder using the remainder theorem:
f(x) = 3x^4 - 3x^3 + x2 - 6x + 2 divided by (x + 7)

Answer 1

x+7 = 0
x = -7
so, the remainder of f(x) when divided by (x+7) is f(-7)

f(x) = 3x^4 - 3x^3 + x2 - 6x + 2
f(-7) = 3(-7)^4 - 3(-7)^3 + (-7)^2 - 6(-7) + 2 = ...

Answer 2

-14

Answer 3

?

Answer 4

can you show to me how you got -14 ??

Answer 5

-2 times 7

Answer 6

wait hold on

Answer 7

probably mistake

Answer 8

the start is here :
3(-7)^4 - 3(-7)^3 + (-7)^2 - 6(-7) + 2 = ...

Answer 9

ok

Answer 10

idk

Answer 11

multiply?

Answer 12

3(-7) = -21 ^4 =-84-3=-87

Answer 13

to get good answer, do them one by one
(-7)^4 = ... then times 3, get ....
-3(-7)^3 = ....
(-7)^2 = ...
-6 * -7 = ...
get the total aobve, then add 2

Answer 14

so -84 for first

Answer 15

second =63

Answer 16

third -14

Answer 17

last 42

Answer 18

(-7)^4 = -7 x -7 x -7 x -7 = 2401

Answer 19

then what

Answer 20

3(-7)^4 = 3 * 2401 = 7203

Answer 21

thats the answer 7203?

Answer 22

it just for the first :p

Answer 23

this's the 2nd -3 (-7)^3 = ...
see that (-7)^3 = -7 x -7 x -7 = -343
so,
-3(-7)^3 = -3 x -343 = 1029

Answer 24

ok then?

Answer 25

next
(-7)^2 = -7 x -7 = 49

Answer 26

next
-6(-7) = 42

Answer 27

yep

Answer 28

see all calcution above is positive
now find the total,
f(-7) = 3(-7)^4 - 3(-7)^3 + (-7)^2 - 6(-7) + 2 = ...
f(-7) = 7203 + 1029 + 49 + 42 + 2 = .......................

Answer 29

-12,647

Answer 30

the 1st

Answer 31

whats the answer cuz I dont get it

Answer 32

7203 + 1029 + 49 + 42 + 2 = ........
if still confuse, use the calculator

Answer 33

8,325?

Answer 34

is that the final answer

Answer 35

yeah, correct!

Answer 36

good!

Answer 37

can you help me with 1 more

Answer 38

sure, if i can :P

Answer 39

Use the Factor Theorem to determine if
x - 5 is a factor of f(x) = x^4 - 8x^3- 45x^2 + 524x - 1120.


Yes, x - 5 is a factor of f(x).

No, x - 5 is not a factor of f(x).

Answer 40

its no right?

Answer 41

to knowing it is right or not, lets check it
f(x) = x^4 - 8x^3- 45x^2 + 524x - 1120
if (x-5) is one of the factor, then f(5) must be equal zero

x^4 - 8x^3- 45x^2 + 524x - 1120
(5)^4 - 8(5)^3- 45(5)^2 + 524(5) - 1120
= 625 - 8(125) - 45(25) + 524(5) - 1120
= 625 - 1000 - 1125 + 2620 - 1120
= ... (this for you)

Answer 42

true

Answer 43

its no

Answer 44

if = 0, yes it is true
if not equal 0, its not true

Answer 45

it equals 0

Answer 46

then say its "TRUE"

Answer 47

is that right though

Answer 48

that Yes, x - 5 is a factor of f(x).?

Answer 49

yeah, i got calculation above equal 0
then
Yes, x - 5 is a factor of f(x)

Answer 50

ok cool thanks

Answer 51

you're welcome

Answer 52

:)