Question

I need help on this..... please ​

Answer 1

`q(x)=2x-5,x\\eq-2`

Explanation:

So we have:

`a(x)=2x^2-x-10\\b(x)=x+2`

And we want to find the quotient q(x). Thus:

`q(x)=(a(x))/(b(x))`

Substitute:

`q(x)=(2x^2-x-10)/(x+2)`

Factor the numerator:

`2x^2-x-10\\=2x^2+4x-5x-10\\=2x(x+2)-5(x+2)\\=(2x-5)(x+2)`

Substitute:

`q(x)=((2x-5)(x+2))/(x+2)`

The (x+2)s cancel out. Therefore:

`q(x)=2x-5`

However, we must restrict x such that it cannot equal -2.

In the original equation, if it did, our answer would be undefined. Thus, our final answer is:

`q(x)=2x-5,x\\eq-2`

And we are done :)

Edit: Typo