Question

Factorize : 3t^3 +4t^2 - 5t - 2 = 0

Answer 1

What does factorize mean?

Answer 2

search on google.

Answer 3

Why can't you search on google?

Answer 4

b'coz i know what it means.

Answer 5

Well why can't you answer the question then? I'm just asking for additional info.

Answer 6

factorize means to express an equation as a product of it factors.

Answer 7

So factorize means factor?
3x^3 +4t^2 - 5t - 2 = 0

Answer 8

-.-,

Answer 9

@Preetha Help!!

Answer 10

You can't factor that equation btw.

Answer 11

Do you know synthetic division?

Answer 12

Do you know how to spot possible rational zeros?

Answer 13

is that supposed to be an x or a t at the beginning?

Answer 14

no

Answer 15

but i know synthetic division

Answer 16

steps pls.

Answer 17

Hey @robtobey he needs to understand how to get those factors

Answer 18

Also @shubham.bagrecha which equation are we solving?

Answer 19

both are same.

Answer 20

anyone of your choice

Answer 21

They aren't the same ...

Answer 22

the 1st eq. is obtained by movin 1/t to LHS and taking LCM.

Answer 23

\[3t^2+4t-5=\frac{1}{t}\]
Assume t does not equal 0
Multiply t on both sides
\[3t^3+4t^2-5t=1\]
Now subtract 1 on both sides

Answer 24

where is that robot guy??
he deleted his post.

Answer 25

@shubham.bagrecha yes that is how you multiply both sides by t

Answer 26

now what is 1/t * t

Answer 27

not 2

Answer 28

ok

Answer 29

but still
what are the factors

Answer 30

????

Answer 31

The only way I see is approximating the solutions
Like you go through the possible rational zeros:
\[\pm1 , \pm 3 , \pm \frac{1}{3}\]
you will see that none of these work

Answer 32

Do you know log operations?

Answer 33

@myininaya the 2 in the equation is correct.

Answer 34

which equation are we looking at?

Answer 35

the first one

Answer 36

i wrote the second one wrong.

Answer 37

Ok.
So do you know how to spot the rational zeros now?

Answer 38

\[t(3t^{2}+4t-5)=2\] So can we write it as-

Answer 39

\[t/2(3t^{2}+4t-5=0)\]

Answer 40

Like you look for possible factors of -2
and 3
And then do the possible factors of -2 over 3
Like this :
\[\pm 1, \pm 2 , \pm 3 ,\pm \frac{2}{3}\]

Whenever you have
\[ax^n+...+b=0\]
To find possible rational zeros you do
you write the poss. factors of a , of b , and then poss of b / poss of a

So

We can start we any of those possible zeros and use synthetic division to find the other quadratic factor if a rational zero exist

Answer 41

You can't do that @shubham.bagrecha Because 2/2=1 not 0

Answer 42

ok

Answer 43

So you said you knew how to do synthetic division right?

Answer 44

yes

Answer 45

Try the possible rational zeros I have above and see if one works

Answer 46

one of them*
one not to be confused with that 1 I have up there

Answer 47

ok

Answer 48

oops missed a possible rational zero
\[\pm \frac{1}{3}\]

Answer 49

some*

Answer 50

\[poss. factors of -2, poss. factors of 3, \frac{ poss. factors of -2}{poss. factors of 3}\]

Answer 51

just explaining why those were missing from above

Answer 52

Have you tried 1 yet ?

Answer 53

no

Answer 54

What did you get when you tried 1?

Answer 55

@shubham.bagrecha you are almost there :)

Answer 56

wait

Answer 57

leaving it here.sorry

Answer 58

you are almost there i promise

Answer 59

Like doing t=1
1 | 3 4 -5 -2
|
--------------------------
|

Bring down the 3

1 | 3 4 -5 -2
|
--------------------------
3 |

Do that 1 times that 3


1 | 3 4 -5 -2
| 3
--------------------------
3 |

Add the ones in the column 4+3


1 | 3 4 -5 -2
| 3
--------------------------
3 7 |

Can you finish this part?