My Math Forum Polynomial Factoring Question

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 May 19th, 2018, 04:45 AM #1 Newbie   Joined: May 2018 From: United States Posts: 6 Thanks: 0 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
 May 19th, 2018, 05:23 AM #2 Math Team   Joined: Jul 2011 From: Texas Posts: 2,885 Thanks: 1504 both factorizations are correct ... $(x-3y)(x-y) = (-1)(3y-x) \cdot (-1)(y-x) = (-1)(-1) \cdot (3y-x)(y-x) = (1) \cdot (3y-x)(y-x) = (3y-x)(y-x)$ Thanks from Ebba Sen Pai
 May 19th, 2018, 01:05 PM #3 Global Moderator   Joined: May 2007 Posts: 6,730 Thanks: 689 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. Thanks from Ebba Sen Pai

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