You can put this solution on YOUR website! When doing these kinds of problems, always factor everything first! Then see if something cancels out.
6x^2 - 31x + 5 = (6x+1)(x-5)
(6x-1)(x-5)
-----------
(x-5)
(x-5)s cancel out.
6x-1 is what you are left with. Be sure to state that x cannot equal 5.
For this one you'll have to long divide since the numerator is not factorable.
x-1 | x^3 + 2x^2 -3x + 2
How many times does x go into x^3?
x^2 <---- Remember
So x^2(x-1) = x^3 - x^2
x^3 + 2x^2 - 3x + 2 -(x^3 - x^2) = x^2 -3x + 2
x-1 | 3x^2 -3x + 2
How many times does x go into 3x^2?
3x <---- Remember
x(x-1) = 3x^2 -3x
3x^2 -3x + 2 - (3x^2 - 3x)
2
How many times does x-1 go into 2? Doesn't make sense.
So we are left with a remainder of 2 or ... 2/x-1 <-- Remember
Putting it all together we have
Be sure to state that x cannot equal 1.
