Question

A polynomial f and a factor of f are given. Factor f completely.

f(x)=x^3-3x^2-16x-12;x-6

Answer 1

familiar wid synthetic division ?

Answer 2

yes i got (x-6)(x+2)(x+1) is that correct?

Answer 3

Yes ! good job :)

Answer 4

Im having trouble with this problem

f(x)=4x^4+26x^3-8x^2+39x-21;x+7

Answer 5

use synthetic division,
divide x+7

Answer 6

i am but its turning out to be big numbers and not equal to 0

Answer 7

-7 | 4 26 -8 39 -21
|
--------------------------------------
4

Answer 8

lets work it and see wat we get

Answer 9

-2, -22,238

Answer 10

-7 | 4 26 -8 39 -21
| -28
--------------------------------------
4 -2

Answer 11

fine so far ?

Answer 12

-7 | 4 26 -8 39 -21
| -28 14 -42 21
--------------------------------------
4 -2 6 -3 | 0

Answer 13

ohh wait nvm i calculated it wrong

Answer 14

so it will be :-
(x+7) (4x^3 - 2x^2 + 6x - 3)

Answer 15

:)

Answer 16

(x+7)(4x^3-2x^2+6x-3)

Answer 17

yes

Answer 18

so do i have to factor it completely....like how

Answer 19

yes you will have to factor it completely

Answer 20

familiar wid rational root theorem ?

Answer 21

yeah but i kinda forgot...is it the one where u list the numbers

Answer 22

4x^3-2x^2+6x-3

Answer 23

yes,

```
rational roots will be of form p/q

p = factors of constant term (3 here)
q = factors of leading coeffecient (4 here)
```

Answer 24

factors of 3 = ?
factors of 4 = ?

Answer 25

1,3
1,2,2,4

Answer 26

plus and minus

Answer 27

yes,

so possible rational roots are :-

\(\pm( 1, ~3, ~2, ~4, ~1/2, ~1/4, ~3/2,~ 3/4)\)

Answer 28

ok...then what

Answer 29

start by testing all possible POSITIVE roots first
start wid +1

Answer 30

ohhh

Answer 31

4x^3-2x^2+6x-3

put x = 1 above, do u get 0 ?

Answer 32

wait do use the 4,-2,6,-3?

Answer 33

dint get u :|

Answer 34

like do i use the synthetic division with 4 -2 6 -3 | 0 or with the original which is 4,26,-8,39,-21

Answer 35

we got the depressed cubic equation,
so we need to work on this cubic oly

use 4 -2 6 -3

Answer 36

ok so 1 doesnt work

Answer 37

wat about 2, 3, 4 ?

Answer 38

does any of it work ?
i dont think so...

try \(1/2\)

Answer 39

yeah it works

Answer 40

good, whats the depressed quadratic after division wid -1/2 ?

Answer 41

4x+6

Answer 42

no, you should get a quadratic.
show me ur synthetic division

Answer 43

4x^2+0+6x

Answer 44

oh you mean
4x^2 + 6 ?

Answer 45

yeah yeah im sorry

Answer 46

its 4x^2 + 0x + 6 ok

Answer 47

np :)

so, 4x^3-2x^2+6x-3 = (x-1/2)(4x^2+6)

Answer 48

yes so its (x+7)(x-1/2)(4x^2+6)

Answer 49

4x^4+26x^3-8x^2+39x-21 = (x+7)(x-1)(4x^2 + 6)

Answer 50

Yes !
dont leave it like that, u can factor further the last quadratic factor aswell

Answer 51

4x^2 + 6 = 2(2x^2+3) = ?

Answer 52

idk..

Answer 53

how would u factor that

Answer 54

use quadratic formula and find zeroes of 2x^2 + 3

Answer 55

a = 2
b = 0
c = 3

Answer 56

\(\large x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}\)

Answer 57

i got