Question

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?

Answer 1

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)`