mathematics

5. P(x) = x - x - 7x + x + 6:0 = 3 F. Read and answer the following problems. 1. What possible polynomial expression can be formed such that -1, 2, -3, and 3 are roots of P(x)? 2. A box manufacturing company models the volume of a box (in cubic inches) they produce to be 6x - 35x2 - 41x + 210. If the height of a box is x - 6, what are the dimensions of the rectangular base of the box? 3. The volume in cubic feet of one popular size practice swimming pool is given by the polynomial V(x) = n(x3 - 5x2 - 86x + 360). What are the dimensions of the pool? If x = 33, is this close to the volume of an Olympic size pool which has an approximate volume of 27 095x cubic feet (ft3)? 4. When P(x) is divided by x - a, the remainder is given by P(a). Find an expression for the remainders when P(x) is divided by bx - a and bx + a, respectively. 5. Suppose n is a positive integer. Determine the values of n that will make x + y a factor of x" - y"