Algebra 2
posted by Peter .
When two rational expressions are divide, the quotient is 5x² + 3x + 12 + 7/(x + 5. What are the two polynomials?

The expression above is a rational expression, not a quotient.
A quotient is just a polynomial, and does not include the division.
Take another look at the problem and post it as it says. 
You are missing a closing bracket
Work backwards by finding a common denominator ...
5x² + 3x + 12 + 7/(x + 5)
= [5x^2(x+5) + 3x(x+5) + 12(x+5) + 7]/(x+5)
= (5x^3 + 25x^2 + 3x^2 + 15x + 12x + 60 + 7)/(x+5)
= (5x^3 + 28x^2 + 27x + 67)/(x+5)