Can someone please explain this?
(x-2)f(x)=x^3 - 4x^2 - 11x + 30
By comparison we take
f(x)=x^2 + bx + c
(x - 2)(x^2 + bx + c) = x^3 - 4x^2 -11x + 30
Therefore
bx^2 - 2x^2 = -4x^2
x^2(b - 2) = -4x^2
Thanks!
+37103 Divide both sides by (x-2)
to get
f(x) = x^2-2x-15 or f(x) = (x-5)(x+3)
+37103 Divide both sides by (x-2)
to get
f(x) = x^2-2x-15 or f(x) = (x-5)(x+3)
+129842 (x-2)f(x)=x^3 - 4x^2 - 11x + 30
I believe that we want to find "f(x)" ......we can do this using polynomial long division
x^2 - 2x -15
x - 2 [ x^3 - 4x^2 - 11x + 30 ]
x^3 - 2x^2
----------------------------------
-2x^2 - 11x
-2x^2 + 4x
---------------------
-15x + 30
-15x + 30
-----------------
0
So....f(x) = x^2 - 2x - 15
And notice that this can be factored as ( x -5) (x + 3)
So
x^3 - 4x^2 - 11x + 30 = (x -2) f(x) = (x -2) ( x^2 - 2x - 15) = (x -2) (x -5) (x + 3)
