Answers to 14 and 34

#14
In order to find forumlas for the graph, we would need to find teh zeroes or the factors of the polynomial.The factors are (a+3)(a-1)(a-5) now by looking at the graph we would have to determine the sign changes. The signs chaneg between the iintervals except for (-infinity,-3) so that factor would be raised to a even power to prevent the sign change. So one equation for the graph would be y=2/5((a+3)^2(a-1)(a-5)). To find another equation for the graph, i just raised teh factor (a+3) to the 4th power. So a second equation would be y=2/225((a+3)^4(a-1)(a-5)).

#34
To find the remainder of the division of the the two polynomials, simply use the remainder theorem. Find the zero of the the divisor (x-1) and substitute that value into the dividend for the x value. So (1-1)=0---> (1)^27+(1)^24+(1)^21...(1)^3+1=10 So the reminder of the quotient would be 10 or 10/(x-1).