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Polynomial Factoring and Solving Equations | Mathematics Practice Questions

Practice polynomial factoring, equation solving, area calculations, and more with these math problems. Strengthen your algebra skills!

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Polynomial Factoring and Solving Equations | Mathematics Practice Questions

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  1. Jeopardy 1 6 11 16 21 26 2 7 12 17 22 27 3 8 13 18 23 28 4 9 14 19 24 29 5 10 15 20 25 30

  2. x 2 y2 – 4x + 9x – 5x 2 y 2 1

  3. Evaluate f(x) = 2x 3 – x 2 – 5x +2 when x = -2 2

  4. Multiply and simplify ( 2x + 1) (5x – 7) 3

  5. ( 5 – 3x) 2 Is it a perfect square ? 4

  6. Simplify 2xy7 . 7xy 5

  7. Factor completely 3x 2 + 7x - 20 6

  8. Factor by grouping 2x 3 + x 2 - 10x - 5 7

  9. Factor the polynomial 5x 4 – 5x 2 8

  10. Factor x 3 + 8 9

  11. Identify the degree and the leading coefficient of the polynomial 5 – 4x + x 3 10

  12. Use factoring to solve the polynomial equation 5x 2 = 15x 11

  13. Whether a trinomial is a perfect square and solve it 4t 2 - 4t + 1 = 0 13

  14. Solve z , 2z 4 - 8z 2 = 0 14

  15. Could the graph of a polynomial function be a line ? 15

  16. Evaluate the polynomial- 4x 2 when x = 2 16

  17. Simplify A rectangular pen has a perimeter of 50 feet. If x represents its width, write a polynomial that gives the area of the pen in terms of x 17

  18. (a 2 + 3b)(a 4 – 3a 2 b + 9b 2) are the factors of a 6 + 27 b 3 18

  19. Factor completely x 2 - 5x - 50 19

  20. If a golfball is hit upward with a velocity of 66 feet per second (45 mph), its height h in feet above the ground after t seconds can be modelled by h(t) = - 16t 2 + 66t. Determine when the ball strikes the ground. 20

  21. A rectangle has an area of 216 square inches. Its length is 6 inches more than its width. Find the dimensions of the rectangle. 21

  22. Factor out greatest common factor 18x 3 + 6x 22

  23. Symbolic representation ‘ Multiply x by the quantity 3 plus 2 23

  24. If you factor the trinomial x 2 + 3x + 2, do you obtain (x + 1)(x + 2) 2 ? Explain 24

  25. Find the least common multiple of 36, 24, 16 25

  26. If xy = 0, does it follow that either x = 0 or y = 0 ? Explain 26

  27. Give one reason for factoring expressions in mathematics 27

  28. Find an expression that represents the product of the sum and difference of two numbers. Let the two number be x and y 28

  29. Find the least common multiple x 2 - 9, x(x + 3) 29

  30. 3x(y – 6) = 0, what property you will use to find x, y ? 30

  31. 5x - 4x 2 y2 1

  32. - 8 2

  33. 10x 2 – 9x – 7 3

  34. 9x 2 – 30x + 25 4

  35. 14x 2 y8 5

  36. (x + 4) (3x – 5) 6

  37. (2x + 1)(x 2 - 5) 7

  38. 5x 2 (x – 1)(x + 1) 8

  39. (x + 2)(x 2 - 2x + 4) 9

  40. 3 ; 1 10

  41. 0; 3 11

  42. Yes ; (2t – 1) 2 13

  43. -2, 0, 2 14

  44. - 16 16

  45. 25x - x 2 17

  46. Yes 18

  47. (x – 10)(x + 5) 19

  48. After 4.125 sec 20

  49. 12 in x 18 in 21

  50. 6x ( 3x 2 + 1) 22

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