SOLUTION: What are the steps to factor the expression x^2-(a+b)x+ab down to (x-a)(x-b)?

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Question 845408: What are the steps to factor the expression x^2-(a+b)x+ab down to (x-a)(x-b)?
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Look at corresponding parts?

x%5E2-rx%2Bp=%28x-a%29%28x-b%29=x%5E2-ax-bx%2Bab=x%5E2-%28a%2Bb%29x%2Bab.
MUST be, r=a+b and p=ab.
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You could try to divide the given trinomial by either x-a or by x-b and see what is the quotient. Any remainder?

Polynomial Division:

______________|_____x___________-b
__________________________________________________
(x-a)_________|____x^2________-(a+b)x________ab
______________|_____x^2_______-ax
______________|_______________________
______________|_____0___________-bx
______________|_________________bx___________ab
______________|_________________0____________0, DONE.
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The quotient is x-b, and remainder is 0.