Thread: Questions Involving Dividing Polynomials

1) 8x^3 + 10x^2 - px - 5 is divisible by 2x+1. There is no remainder. Find the value of p.

2) When x^6 + x^4 - 2x^2 + k is divided by 1 + x^2, the remainder is 5. Find the value of k.

3) The volume of a cylindrical can is (4πx^3 + 28πx^2 + 65πx + 50π) cm^3. The can is (x +2) cm high. What is the radius?

If anyone can help me out with any of these questions I would really appreciate it! Thanks in advance! Just to clarify, "π" is pi.

1.) Let

From the given information, we know from the remainder theorem we must have:



From this you can find .

2.) Let and

By the remainder theorem and the given information, we know:



From this you can find .

3.) The volume of the can is:



From this you may determine . Check to see if the cubic has -2 as a root.

Thank you so much!