Question

Express 6x^3+23x^2-6x-8 in factored form

Answer 1

for the 1st root we will need guess and check...or is anything else, like hint is given ?

Answer 2

after we find 1st root, its just the matter of synthetic division

Answer 3

Um okay

Answer 4

like check for
x=1,-1,2,-2,3,-3,4,-4....
if for any of these, f(x) comes out to be 0, then we get our 1st root.

Answer 5

Isn't there an easier way to do it, like a faster way ?

Answer 6

yes, there is a theorem, rational root theorem, heard of it ?

Answer 7

it simplifies guessing of a root

Answer 8

Oh could you show me how to do it then?

Answer 9

sure,
if \( f(x)=ax^3+bx^2+cx+d \)
then a possible rational root will be reduced form of \(\huge \pm \dfrac{d}{a}\)

Answer 10

plus or minus , last term (constant) divided by co-efficient of highest power of x

Answer 11

so, what can you guess about the possible rational root of
6x^3+23x^2-6x-8 ?

Answer 12

getting this ? or went completely overhead? :P

Answer 13

Im soo lost omg. LOL Could you write it out? and maybe I'll understand step by step

Answer 14

.. 6x^3 + 23x^2 - 6x - 8
= 6x^3 + ( 24 - 1 ) x^2 - ( 2 + 4 ) x - 8
= 6x^3 - x^2 + 24x^2 - 2x - 4x - 8
= (6x^3 - x^2 - 2x) + (24x^2 - 4x - 8)
= x (6x^2 - x - 2) + 4 (6x^2 - x - 2)
= (x + 4) (6x^2 - x - 2)
= (x + 4) (2x + 1) (3x - 2)

Answer 15

for the second line. Where does the 24 - 1 and 2+4 come from?

Answer 16

ok, for example, the equation
2x^2+3x+7
will have a possible rational root of 7/2

Answer 17

where does that comee from? :(

Answer 18

7/2