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when combining like terms, do i do 3x^2 plus negative 2x^2? or does the sign change to addition, 3x^2 plus 2x^2?

when combining like terms, do i do 3x^2 plus negative 2x^2? or does the sign change-example-1
User GJDK
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1 Answer

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Let's start using this property:


(a)/(b)+(c)/(b)=(a+c)/(b)

In this case:


\begin{gathered} a=3x^2-2x-1 \\ c=-2x^2+x-5 \\ b=x-5 \\ so\colon \\ (3x^2-2x-1)/(x-5)+(-2x^2+x-5)/(x-5)=((3x^2-2x-1)+(-2x^2+x-5))/(x-5) \end{gathered}

Now, let's add like terms in the numerator:


\begin{gathered} (3x^2-2x-1-2x^2+x-5)/(x-5)=((3x^2-2x^2)+(-2x+x)+(-1-5))/(x-5) \\ \to(x^2-x-6)/(x-5) \end{gathered}

For the numerator:


x^2-x-6

The factors of -6 that sum to -1 are 2 and -3, therefore:


x^2-x-6=(x+2)(x-3)

Hence:


(x^2-x-6)/(x-5)=((x+2)(x-3))/(x-5)

User The Pointer
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