Polynomial division help (1 Viewer)

[Brodie28]

I was asked to write this as a product of its factors...

x³ - 7x + 6

After dividing by (x-1) I got x² - x - 6

With division transformation it became

(x - 1)(x² - x - 6) broken down into
(x - 1)(x + 2)(x - 3)

Is this correct? The text book got (x - 1)(x - 2)(x + 3)
Iv checked it a few times and still get the same answer...

 

[FinalFantasy]

I was asked to write this as a product of its factors...

x³ - 7x + 6

After dividing by (x-1) I got x² - x - 6

With division transformation it became

(x - 1)(x² - x - 6) broken down into
(x - 1)(x + 2)(x - 3)

Is this correct? The text book got (x - 1)(x - 2)(x + 3)
Iv checked it a few times and still get the same answer...

(x - 1)(x² - x - 6)=x³-x²-6x-x²+x+6=x³-2x²-5x+6
.: u made an error

 

[Brodie28]

Ill have to go back over it again...

Also... What are linear factors?

 

[..:''ooo]

linear factors are (x-a) etc
quadractic factors are (x^2-a) etc

linear factor gives the roots of equation, be it real or non real

 

[KFunk]

I was asked to write this as a product of its factors...

x³ - 7x + 6

After dividing by (x-1) I got x² - x - 6

With division transformation it became

(x - 1)(x² - x - 6) broken down into
(x - 1)(x + 2)(x - 3)

Is this correct? The text book got (x - 1)(x - 2)(x + 3)
Iv checked it a few times and still get the same answer...

Do it by inspection for cubics, polynomial division sucks. You could try out ruffini's method:

http://en.wikipedia.org/wiki/Ruffini's_rule

If you know that (x-1) is a factor of x³ - 7x + 6 then:

x³ - 7x + 6 = (x-1).G(x)

By inspection you know that G(x) = x² + ax - 6 [since your original polynomial is monic and has a constant term of 6]

You can then observe by looking at parts of the expansion that (-6 + a)x = -7x ---> a = -1
Hence G(x) = x² + x - 6

x³ - 7x + 6 = (x-1)(x² + x - 6) = (x-1)(x-2)(x+3)


P.S (If you were to do it by inspection you wouldn't go through all that stuff on paper but it's an example of the kind of thought process which you might quickly go through. Save yourself from polynomial division )