The document provides step-by-step instructions for solving a polynomial long division problem to get a quotient and remainder of zero. It explains that you first perform the long division, then set the remainder equal to zero and solve the resulting equations to find the values of a and b that make the remainder zero. This gives values of a=4 and b=-11, which when added together equal the solution of -7.

1. Brittany’s POTW Solution

2. The answer to this problem is -7. First you would perform the long division, between the expression and the factor of the expression. This would give you a quotient of ax + (b + 4a), with a remainder of (11a+4b)x+(25-5b-20a). Since the remainder must be zero, set both parts of the remainder equal to zero. (11a+4b)=0 and 25-5b-20a=0. Next solve the second equation for b, getting b=5-4a. Then substitute that expression into the first expression to solve for a. 11a+4(5-4a)=0, which gives you a=4 and b=(-11). Then add 4+(-11) which gives you -7 as your final answer.