factor x^3-5x^2+4x
For this equation you should find that (x+1) is a factor. If you sub 1 in for the x-values you should get a result of zero. So next you do the following:
(x+1) divided by (x^3-5x^2+4x)
- First you divide the (x^3) by (x+1) and you find that in order to get x^3 you must multiple the x in (x+1) by x^2 but if you do so you get the following:
x^3 +1x^2
- you take this number and you subtract from x^3 - 5x^2
x^3-5x^2
x^3+1x^2
---------
0-4x^2
- Now you do the same with the 4x^2; what must you multiple x in (x+1) to get -4x^2; you would multiply it by -4x and as a result you would get the following:
-4x^2-4
- Next, you would subtract this from the following:
-4x^2+4
-4x^2-4
--------
0
Now your factored equation is:
(x+1) ( x^2-4x)
I think I may have done an error here. The expanded form the factored equation does not equal the equation above. Hmmm...I'm going to recheck and get back to you if I figure it out.
I just realized the long division is completely unnecessary. You could just simply factor the x out. -_-
x^3=5x^2+4x
= x(x^2-5x+4)
= x(x-1)(x-4)
Hope this makes more sense. Ignore what I did above. It's completely wrong.
To factor the expression x^3 - 5x^2 + 4x, we can start by looking for common factors among the terms. In this case, we can notice that there is a common factor of x among all terms. By factoring out an x, we get:
x(x^2 - 5x + 4)
Next, we can try to factor the quadratic expression (x^2 - 5x + 4). We need to find two numbers such that their product is equal to the product of the leading coefficient (1) and the constant term (4), and their sum is equal to the coefficient of the middle term (-5).
In this case, the numbers that satisfy these conditions are -1 and -4, as (-1) * (-4) = 4 and (-1) + (-4) = -5.
Using these numbers, we can rewrite the quadratic expression as:
x(x - 1)(x - 4)
Therefore, the fully factored form of the expression x^3 - 5x^2 + 4x is:
x(x - 1)(x - 4)