What is the algebraic expression represents the phrase "the quotient of negative eight and the sum of a number and three"?

You set it up like this.

So quotient means that you're dividing, so put a:

Next, it says the dividend, or the part being divided is - 8, so now you have this: - 8:

Lastly, it says the divisor, or the part doing the dividing, is a quantity equal to the sum of "some number" (we'll use x) and 3. Since the divisor is one quantity collectively, you have to put it in parentheses.

This gives you: (x + 3)

When you put it all together, you get - 8 : (x + 3).

This can also be written as a fraction by putting - 8 over (x+3).