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Different algebra problems

1. The result of dividing x4 - 2x3 + x2 - 3x + 2 by x - 2 is:
A. x3 - x + 1
B. x3 - x - 1
C. x3 + x - 1
D. x3 + x + 1

2. What is the remainder when 4x3 + 5x2 - 13x - 7 is divided by x - 2?
A. -33
B. 19
C. 33
D. 7

Use the Remainder Theorem to find P(c). P(x) = x4 + 3x2 + 1, c = 3
A. 107
B. 109
C. 19
D. 1

4. Are (x - 1) and (x + 4) factors of P(x) = 2x3 + 5x2 - 13x + 4 ?
A. Neither
B. Both
C. Only (x - 1)
D. Only (x + 4)

5. Determine whether -3 and 2 are zeros of P(x) = 2x3 - 5x2 - 4x + 12.
A. Neither
B. Both
C. Only -3
D. Only 2

6. What is the remainder if 7x53 - 3x31 + 19x3 - 13 is divided by x + 1?
A. 10
B. -42
C. -36
D. -13

7. Determine the far-left and far-right behavior of the graph of the polynomial function P(x) = 3x4 - 5x2 + 7.
A. up to the left and down to the right
B. down to the left and down to the right
C. up to the left and up to the right
D. down to the left and up to the right

8. Determine the maximum or minimum range value [P(x)] of the function P(x) = -3x2 + 6x + 5. State whether this value is a maximum or a minimum.
A. 1; minimum
B. 8; maximum
C. 1; maximum
D. 8; minimum

9. Sketch the graph of P(x) = 4x2 - x3.

10. Find the real zeros of the polynomial function P(x) = x(x + 1)(x2 - 81).
A. 0, -1, 9, -9
B. 0, -1, 9
C. -1, 9, -9
D. 0, 1, 9

11. Find all the real numbers that solve: x(x2 + 64) = 0.
A. -8, 0, 8
B. 0, 8
C. -8, 0
D. 0

12. Find all the factors of x3 + 2x2 - 3x.
A. (x-3)(x+1)
B. x(x-3)(x+1)
C. x(x+3)(x-1)
D. (x+3)(x-1)

13. A manufacturer has determined that the revenue received from selling x items of a product is given by R(x) = -0.3x2 + 200x and the cost to produce x items of the product is given by C(x) = 80x + 9400. Assuming that all of the products produced can be sold, how many should be produced to maximize the profit? (Hint: profit = revenue - cost)
A. 0.00125
B. 400
C. 200
D. 33

14. Use the Rational Zero Theorem to list the possible rational zeros of the polynomial 4x4 - 9x2 + 5.

15. Using Descartes Rule of Signs, determine the number of possible positive real roots of the polynomial 3x4 + 5x3 + 8x2 - 7x + 2.
A. 4, 2 or 0
B. 2 or 0
C. 2
D. none

16. With the help of synthetic division, find the zeros of the polynomial 2x3 + 9x2 - 32x + 21.
A. -1/7, 1, 2/3
B. -3/2, -1, 7
C. -7, 1, 3/2
D. -7, -3/2, 1

17. Find all the zeros of the polynomial x3 - 4x2 + 9x - 36.
A. -4, 3i, -3i
B. -3, 4i, -4i
C. 4, 3i, -3i
D. 3, 4i, -4i

18. Write x4 - 6x2 - 27 as a product of linear factors and quadratic factors that are irreducible over the reals.
A. (x2 + 3)(x + 3)(x - 3)
B. (x + 3)2(x - 3)
C. (x2 + 3)(x2 + 9)
D. (x + 3)2(x - 3)2

19. Find a polynomial of degree 3 that has zeros 3, 2, and -1.
A. x3 - 7x - 6
B. x3 - 4x2 + x + 6
C. x3 + 4x2 + x - 6
D. x3 - 6x2 - x + 6

20. Two hundred meters of rope is used to mark off a rectangle (the dimensions are x meters by y meters.
a. Write the equation showing perimeter of 200 using x and y.
b. Write the formula for area using x and y.
c. Write the function for area using only x, which could be used to find the maximum possible area

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