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May 19th, 2018, 04:45 AM   #1
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Math Focus: Algebra
Polynomial Factoring Question

I am consistently getting answers that my book says are wrong, but only in terms of positive or negative signs, with every other thing composing my answer (parenthesis, exponents, coefficients and variables) being consistently correct. The following would be the best representation of what I mean

My Answer: (Midway through problem after using AC to convert my trinomial to a 4 term polynomial)

x²-3xy-xy+3y²

3y(y-x)-x(y-x)

(3y-x)(y-x)


Book Answer

(x−3y)(x−y)

The only difference is that each term in parenthesis has the reversed value in terms of being positive or negative, but I do not understand the reasoning. I can see that I am missing somthing very simple, (unless both answers are correct) but I have no idea what it is
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May 19th, 2018, 05:23 AM   #2
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both factorizations are correct ...

$(x-3y)(x-y) = (-1)(3y-x) \cdot (-1)(y-x) = (-1)(-1) \cdot (3y-x)(y-x) = (1) \cdot (3y-x)(y-x) = (3y-x)(y-x)$
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May 19th, 2018, 01:05 PM   #3
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If you write it as 3y(y-x)+x(x-y), you will see that something has to change sign in order to combine. The choice is arbitrary. You chose one way and the book chose the other.
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