Posted by **kingwendu** on Saturday, December 17, 2011 at 8:26pm.

given that f(x)= 3-7x+5x^2-x^3, factorise the polynomial completely, hence state the set of values of x for which the function is equal or less than zero .

- function -
**Damon**, Saturday, December 17, 2011 at 8:39pm
-1 ( x^3 - 5 x^2 + 7 x - 3)

I can see right away that x = 1 makes this zero because 8-8 = 0

divide polynomial by (x-1)

******_x^2_-_4x____+_3_______________

x-1 / x^3 - 5 x^2 + 7 x - 3

*******x^3 - 1 x^2

*******---------------------

***********- 4 x^2 + 7 x -3

***********- 4 x^2 + 4 x

***********-----------------

*******************+ 3 x - 3

*******************+ 3 x - 3

remainder =0

so

-1 (x-1)(x^2 - 4 x + 3)

so

-1 (x-1)(x-1)(x-3)

zeros at 1, 1 (double,just hits axis) and 3

graph it remembering the - sign

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