Question

Can someone show me the steps to these questions (I will provide the correct answers)? Thanks in advance.

1. When the polynomials 4x^3 + mx^2 + nx + 11 is divided by x + 2, the remainder is -7. When the polynomial is divided by x - 1, the remainder is 14. What are the values of m and n? Answer is: m = 2, n = -3

2. For what value[s] of k does the function f(x) = x^3 + 6x^2 + kx - 4 give the remainder when divided by either x - 1 or x +2? Answer: k = 3

3. When (x^2 + 5x + 7) is divided by (x+k), the remainder is 3. Determine k. Answer: k = 1 or k = 4

Answer 1

The text-only format of Jiskha makes it difficult and messy to illustrate the technigue you need to use, which is called polynomial long division. There is a shorthand form called synthetic division. I suggest you review both, using Google to search for sites that illustrate the methods. The method of solution will be to see what values of the constant(s) either result in no remainder or the specified remainder. If you had just posted one question, I'd be glad to work it through for you, but three is too many.