SOLUTION: How do I factor this to get all the x's? {{{x^3 -5x^2 + 7x -3}}} I tried long division and grouping, neither worked.

Algebra ->  Expressions-with-variables -> SOLUTION: How do I factor this to get all the x's? {{{x^3 -5x^2 + 7x -3}}} I tried long division and grouping, neither worked.       Log On


   

Question 904633: How do I factor this to get all the x's?
x%5E3+-5x%5E2+%2B+7x+-3
I tried long division and grouping, neither worked.
Found 2 solutions by MathLover1, jim_thompson5910:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

++x%5E3-5x%5E2+%2B7x-3+...write -5x%5E2 as -2x%5E2-3x%5E2 and 7x as x%2B6x
++x%5E3-2x%5E2%2Bx+-3x%5E2%2B6x-3+ ...group

++%28x%5E3-2x%5E2%2Bx%29+-%283x%5E2-6x%2B3%29+

++x%28x%5E2-2x%2B1%29+-3%28x%5E2-2x%2B1%29+

+%28x-3%29+%28x%5E2-2x%2B1%29+ ...in %28x%5E2-2x%2B1%29+ write -2x as -x-x
+%28x-3%29+%28x%5E2-x-x%2B1%29+
+%28x-3%29+%28%28x%5E2-x%29-%28x-1%29%29+

+%28x-3%29+%28x%28x-1%29-1%28x-1%29%29+

+%28x-3%29+%28x-1%29%28x-1%29+
or, you can put it this way
+%28x-3%29+%28x-1%29%5E2+


Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
If you graph y+=+x%5E3+-5x%5E2+%2B+7x+-3, you get



The graph has the x-intercepts of x+=+1 and x+=+3

Since the graph touches the x axis at x+=+1 and doesn't pass through it, this means we have a root with multiplicity of 2 here.

So the factorization is %28x-1%29%5E2%2A%28x-3%29