SOLUTION: Can someone please check my work, seems like I missed a step. factor completely x^3-26x^2+48x =x(48+-26x+x^2 x(2+1-1x)(24+-1x) Thank you

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Question 31775: Can someone please check my work, seems like I missed a step.
factor completely
x^3-26x^2+48x
=x(48+-26x+x^2
x(2+1-1x)(24+-1x)
Thank you
Found 2 solutions by atif.muhammad, mbarugel:
Answer by atif.muhammad(135)   (Show Source): You can put this solution on YOUR website!
x^3-26x^2+48x
=x(48+-26x+x^2
x(2+1-1x)(24+-1x)

I'd have done it this way:
x^3-26x^2+48x = x(x^2-26x+48) = x(x^2-24x-2x+48) -->This is called 'splitting the middle term' technique
Let's factorise the quadratic
x^2 - 24x - 2x + 48
x(x-24)-2(x-24)
(x-2)(x-24)
Let's join up the quadratic with the rest of the expression
x(x^2-26x+48) = x(x^2-24x-2x+48)=x(x-2)(x-24)
Answer by mbarugel(146)   (Show Source): You can put this solution on YOUR website!
Hello!
Your work has a slight mistake.
You have expression
Taking x as common factor:

Now you can factorise the quadratic equation inside using its roots. The roots of this equation are 24 and 2:
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=484 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 24, 2. Here's your graph:


Therefore,

So the whole expression becomes:


I hope this helps!
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