Factorising cubics

Oh the joys of additional maths...
I'm really confused on how to factorise cubics, they are new to me and well the teacher either didn't explain them amazingly or I zoned out.... So if this is the question, how would you factorise it?
6x³-13x²+x+2 is divided by (x-2). The remainder is 0, so I know that (x-2) is a factor. I also know you have to do this:-
(x-2) (6x³-13²+1) but how do I factorise the bracket with the cubic?
Thanks for any help.. :smile:

)

Reply 1

Lilmzbest

Original post by Phoebe♥

Oh the joys of additional maths...
I'm really confused on how to factorise cubics, they are new to me and well the teacher either didn't explain them amazingly or I zoned out.... So if this is the question, how would you factorise it?
6x³-13x²+x+2 is divided by (x-2). The remainder is 0, so I know that (x-2) is a factor. I also know you have to do this:-
(x-2) (6x³-13²+1) but how do I factorise the bracket with the cubic?
Thanks for any help.. :smile:

)

The problem is that you've written the second line wrong, if you multiply out the brackets you will see that you do not get the original cubic

Try long division :smile:

Reply 2

TenOfThem

18

Original post by Phoebe♥

Oh the joys of additional maths...
I'm really confused on how to factorise cubics, they are new to me and well the teacher either didn't explain them amazingly or I zoned out.... So if this is the question, how would you factorise it?
6x³-13x²+x+2 is divided by (x-2). The remainder is 0, so I know that (x-2) is a factor. I also know you have to do this:-
(x-2) (6x³-13²+1) but how do I factorise the bracket with the cubic?
Thanks for any help.. :smile:

)

You know one bracket (x-2) you just have to figure the rest

(x-2)(6x^2 + ?x - 1)

You need the

6x^2

to multiply with the x
You need the -1 to multiply with the -2

When you multiply -2 by

6x^2

you get

-12x^2

and you will need another

-1x^2

SO the x multiplied by the ?x will give you that if ? is -1

So you have

(x-2)(6x^2 - x - 1)

You should know how to factorise a quadratic

Reply 3

Hasufel

16

you know that

(x-2)

is a factor, so use the fact that:

6x^{3}-13x^{2}+x+2=(x-2)(ax^{2}+bx+c)

expand the right side, and equate the coefficients of like powers.

Reply 4

upthegunners

10

Original post by Phoebe♥

Oh the joys of additional maths...
I'm really confused on how to factorise cubics, they are new to me and well the teacher either didn't explain them amazingly or I zoned out.... So if this is the question, how would you factorise it?
6x³-13x²+x+2 is divided by (x-2). The remainder is 0, so I know that (x-2) is a factor. I also know you have to do this:-
(x-2) (6x³-13²+1) but how do I factorise the bracket with the cubic?
Thanks for any help.. :smile:

)

divide