Question: 5. Solve for x, XER. Be sure to include justification for your solution. a) (x+1)(x-2)(x-4) 2 > 0 b)-x 3 + 25x < 0 6.
5. Solve for x, XER. Be sure to include justification for your solution.
a) (x+1)(x-2)(x-4)2 > 0
b)-x3 + 25x < 0
6. If f(x) = x3-(a+b)x2 + abx, find the value of f(a) and explain the significance of x - a.
7. When 2x3 + kx2 - 5x + 1 is divided by (x-2), the remainder is 19. Find the value of k.
8. A rectangular piece of cardboard that has dimensions 20 cm X 10 cm will be formed into an open top cardboard box. The corners of the piece of cardboard, in the shape of a square, will be removed. If the desired volume of the cardboard box is to be 144 cm3, what will be the dimensions of the cardboard box? Where applicable, round to the nearest one hundredth of a cm (ie. round to two decimal places).
9. When 2x3 + x2 - 2kx + f divided by x-1 , the remainder is -4, and when it is divided by, x+2 the remainder is 11. Determine the values of "k" and "f"
10. Determine an expression forf(x) in whichf(x) is cubic, f(x) > 0 when x<2, f(x) < 0 when x-2 and f(0) = 4. Be sure to show your thinking and/or explain your reasoning for your answer.
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