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?

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- May 13th 2009, 03:44 AManon_404Factorize
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? - May 13th 2009, 05:41 AMTheMasterMind
- May 13th 2009, 05:46 AManon_404
- May 14th 2009, 06:02 AMcraig
Synthetic Division

There is a good example on synthetic division found here. - May 14th 2009, 07:18 AMe^(i*pi)
- May 14th 2009, 12:23 PMHallsofIvy
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

$\displaystyle x^3- 9x^2+ 24x+ 16= (x-1)(x^2- 8x- 16)$

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

$\displaystyle (x-1)(x^2- 8x- 16)= (x)(x^2- 8x- 16)- (x^2- 8x- 16)$

$\displaystyle = x^3- 8x^2- 16x- x^2+ 8x+ 16= x^2- (8+1)x^2- (16-8)x+ 16$

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

Quote:

And what are the values of x?

In this case you can also factor $\displaystyle x^2- 8x- 16= (x- 4)^2$ so

$\displaystyle x^3- 8x- 16= (x- 1)(x^2- 8x- 16)= (x-1)(x-4)^2= 0$ 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]