Question

How do you divide `(3x^2+7x-20) / (x+4)`?

Answer 1

`3x-5`

Explanation:

Hint: If you see the question carefully, you might notice that the question was intended so that you may have to factor the numerator in such a way that `x + 4` is a factor, and gets cancelled with the denominator. Let's try doing that.

Let `N = 3 x^2 + 7 x - 20`.
Note that `3x(x+4) = 3x^2 + 12x`

Thus, we write:
`N = 3 x^2 + 12 x - 5x - 20 = 3x (x+4) -5 (x+4) = (3x-5) (x+4)`

Now we come to the question itself
`( 3 x^2 + 7 x - 20 ) / ( x + 4 ) = ( (3x-5) cancel((x+4)) ) / cancel((x+4)) = 3x-5`