Question

Help me solve this!

Answer 1

\[t^3-6t+11t-6=0\]

Answer 2

Could you explain me the steps? @jim_thompson5910 @Loser66 @mathmale @mathmate @phi @satellite73 @zepdrix @Zenmo @TheSmartOne

Answer 3

-6t or -6t^2 ?

Answer 4

uhh 1,-6,11

Answer 5

you might have a typo @HELP!!!!

Answer 6

Is the question:

\[t^3-6t^2+11t-6=0\]

OR

\[t^3-6t+11t-6=0\]

Answer 7

ohh its t^3-6t^2+11t-6

Answer 8

\[t^3-6t^2+11t-6\]

Answer 9

@jim_thompson5910

Answer 10

ok so the coefficients for \(\Large t^3-6t^2+11t-6\) are what?

Answer 11

1, 6, 11

Answer 12

-6

Answer 13

hint: think of \(\Large t^3-6t^2+11t-6\) as \(\Large 1t^3-6t^2+11t-6\)

Answer 14

it should be 1,-6,11,-6

Answer 15

when you add up all of those coefficients, what do you get?

Answer 16

6

Answer 17

no

Answer 18

Wait what? Could you elaborate?

Answer 19

wait it would be 0

Answer 20

sorry i should have said

"think of \(\Large t^3-6t^2+11t-6\) as \(\Large 1t^3-6t^2+11t^1-6t^0\) "

Answer 21

yeah when you add up the coefficients, you get 0

Answer 22

whenever that happens, it is guaranteed that 1 is a root

so t = 1 is a root of \(\Large t^3-6t^2+11t-6\)

Answer 23

that means t - 1 is a factor of that :o

Answer 24

use this information to perform long division or synthetic division to find the other roots/factors

Answer 25

gotcha. But how would you factor solve by factoring?

Answer 26

which method has your teacher gone over? polynomial long division? or synthetic division?

Answer 27

None just factoring... Like I know how to solve them either way

Answer 28

so you know synthetic division?

Answer 29

yup!! I can solve it from here. I was just wondering if there was a way to solve it by factoring. Thanks for the help!!

Answer 30

well the idea is that you use synthetic division to factor in the form

(x-1)*p(x)

where p(x) will be some quadratic function. Then you can factor the quadratic or use the quadratic formula to solve p(x) =0. I recommend the quadratic formula