Difference between factoring and dividing polynomials?

Question

Dividing 5x^2+14x-3 by x+3 gives a quotient of 5x-1. Explain why 5x^2+14x-3/x+3 is not the same as 5x-1.?

Answer 1

They are the same.

Factoring does involve dividing.

Take this simple example:

2a + 4

How do you factor?  By finding like terms.  Here it's 2.

2(???)

So what goes in the middle?  The result when you divide 2a + 4 and 2, in this case, is a+2, so:

2(a + 2)

So your:

(5x² + 14x - 3) / (x + 3)

When you factor, you get:

(5x - 1)(x + 3) / (x + 3)

The x+3's cancel, leaving

5x - 1