Thread: Factorize

How does:

x^3 - 9x^2 + 24x -16

Become:

(x - 1) (x^2 - 8x - 16)

And what are the values of x?

What would be good study material for this type of algebra?

Originally Posted by anon_404

How does:

x^3 - 9x^2 + 24x -16

Become:

(x - 1) (x^2 - 8x - 16)

And what are the values of x?

What would be good study material for this type of algebra?

The most efficent way to do this I would presume would be to use the method of synthetic division for dividing polynomials. Have you learned this method?

Originally Posted by TheMasterMind

The most efficent way to do this I would presume would be to use the method of synthetic division for dividing polynomials. Have you learned this method?

I havn't used that method.

Synthetic Division

There is a good example on synthetic division found here.

Originally Posted by anon_404

How does:

x^3 - 9x^2 + 24x -16

Become:

(x - 1) (x^2 - 8x - 16)

And what are the values of x?

What would be good study material for this type of algebra?

Are you sure that's a correct factorisation? Look at the last terms: -1 x -16 = +16 not -16 as stated in the question

Originally Posted by anon_404

How does:

x^3 - 9x^2 + 24x -16

Become:

(x - 1) (x^2 - 8x - 16)

It doesn't! It is easy to see quickly that the constant term in that product is (-1)(-16)= +16, not -16 as in the first expression. It is true that

The best way to see this is to multiply it back:


[tex]= x^3- 9x^2- 8x+ 16[/itex]

And what are the values of x?

??? x can be any number! Did you mean "what are the values of x that make this 0" or "what values of x solve ?

In this case you can also factor so
and you can use the fact that "if ab= 0 then either a= 0 or b= 0".

What would be good study material for this type of algebra?[/QUOTE]