Question

Given the binomials (x - 1), (x - 3), (x + 3), and (x + 5), which one is a factor of f(x) = x^3 + 6x^2 + 12x + 35?

Answer 1

(x - 1)

(x - 3)

(x + 3)

(x + 5)

Answer 2

use factor theorem + synthetic division

Answer 3

if x - 1 is a factor, then the remainder in division will be 0

Answer 4

\[f(x) = x^3 + 6x^2 + 12x + 35? \]
to make it easier to read

Answer 5

u familiar wid synthetic diviosn right ?

Answer 6

somewhat

Answer 7

setup the division

Answer 8

lets test first if x-1 is a factor

1 | 1 6 12 35
|
--------------------------

Answer 9

do u knw the steps ?

Answer 10

not much... I'm guessing divide the terms by -1?

Answer 11

nope, just move the first coefficient 1 down.
make sure u understand the steps cuz u gona test remaining factors :)

Answer 12

1 | 1 6 12 35
|
--------------------------
1

Answer 13

next, multiply this 1 wid the 1 on left and write it down the next coefficient

Answer 14

1 | 1 6 12 35
| 1
--------------------------
1

Answer 15

next add 6 and 1 and write it below

Answer 16

1 | 1 6 12 35
| 1
--------------------------
1 7

Answer 17

repeat the steps :-

miltiply 7 and 1, write it below next coeffecient

Answer 18

1 | 1 6 12 35
| 1 7
--------------------------
1 7

Answer 19

add, multiply, add multiply..... keep going

Answer 20

uhh 1* 12 = 12... 12 + 7 = 19?

Answer 21

1 | 1 6 12 35
| 1 7 19
--------------------------
1 7 19 |54

so remainder is 54, which is not 0. so x-1 is not a factor.

Answer 22

similarly, test next factor

Answer 23

u need to have lots of patience ok -_-

Answer 24

lets test first if x-3 is a factor

3 | 1 6 12 35
|
--------------------------

Answer 25

I see so a lot of testing lol

Answer 26

give it a try

Answer 27

yes after this, two more.

Answer 28

so we want 0 as our remainder?

Answer 29

yes, if u get 0 as remainder, then its a factor.

Answer 30

3 * 1 = 3, 3 + 1 = 4
3 * 6 = 18, 18 + 4 = 22 or is it 6 + 4 = 10?

Answer 31

i want u do the synthetic division *properly* in the synthetic division looking format :)

Answer 32

lol

Answer 33

lets test first if x-3 is a factor

3 | 1 6 12 35
| 3 27 117
-------------------------
1 9 39 | 152

here remainder is 152, which is not 0.
so x-3 is not a factor.

Answer 34

test next guy

Answer 35

lets test first if x+3 is a factor

-3 | 1 6 12 35
|
--------------------------
1

Answer 36

see if u can do this

Answer 37

(in synthetic division format :) )

Answer 38

u gave up ?

Answer 39

-3| 1 6 12 35
| -3 -18-216
---------------------------
-3 -18-216-7560 lol?

Answer 40

I feel like I did something wrong when I ended up with -7560

Answer 41

NO !
u need to add. not multiply

Answer 42

Right...

Answer 43

-3| 1 6 12 35
| -3
---------------------------
-3 3

Answer 44

do it again

Answer 45

now multiply 3 wid left side -3

Answer 46

and write it below 12

Answer 47

-3|1 6 12 35
| -3 3 15
----------------------
-3 3 15 40?

Answer 48

sir, 3*-3 = -9

Answer 49

ah I'm so confused lol

Answer 50

-3|1 6 12 35
| -3 -9
----------------------
1 3

Answer 51

add 12 and -9
write the result below

Answer 52

3

Answer 53

-3|1 6 12 35
| -3 -9
----------------------
1 3 3

Answer 54

multiply this 3 wid left side -3
and write the result below next coefficient.

Answer 55

-3|1 6 12 35
| -3 -9 -9
----------------------
1 3 3

Answer 56

add both

Answer 57

-3|1 6 12 35
| -3 -9 -9
----------------------
1 3 3 | 26

the remainder is 26, which is not 0
so, x+3 is not a factor.

Answer 58

test the last one.

Answer 59

+ 5 is our last one right?

Answer 60

x+5

so u need to put -5 in synthetic division

Answer 61

-5|1 6 12 35
|
----------------------
1

Answer 62

carry out same steps,
u should get 0 this time.
give ur best try :)

Answer 63

alright so first I would multiply 1 * -5 right?

Answer 64

yes

Answer 65

so -5 + 6 now?

Answer 66

which is 1

Answer 67

yes,
synthetic division format please -.-

Answer 68

man that takes forever to draw out lol

Answer 69

copy paste ?

Answer 70

-5|1 6 12 35
|
----------------------
1

Answer 71

-5|1 6 12 35
|
----------------------
1

Answer 72

see it wont take any time :)
copy paste the thing and fill the second and 3rd rows ok

Answer 73

-5|1 6 12 35
| -5 -5 -35
----------------------
1 1 7 | 0

since 0 is the remainder here,
x+5 is a factor.

Answer 74

sorry about that had to answer the phone

Answer 75

ohh ok I see how you did that

Answer 76

Thanks for the help man! Can finally go to the gym now :D

Answer 77

Enjoy the workout cya !