Chapter 8 - Algebra Coach Exercises



Algebra Coach Exercise on factoring expressions with common factors.
Factor each of the following expressions. To do this drag-and-drop each of these problems into the Algebra Coach and click the Factor button.
  1. 10 x - 5 y
  2. 4 x ^ 3 + 3 x ^ 2
  3. x ^ 4 + 3 x ^ 3 - x ^ 2
  4. 2 (a + b) ^ 4 + 5 (a + b) ^ 2
  5. 5 x y ^ 3 - 15 x ^ 3 y + 10 x y
  6. 4 x + 8 x y + 12 x z
  7. 12 x y ^ 2 + 3 x ^ 2 y


Algebra Coach Exercise on factoring expressions with common factors in denominators.
Factor each of the following expressions. To do this drag-and-drop each of these problems into the Algebra Coach and click the Factor button.
  1. 1 / x ^ 3 + 1 / x ^ 5
  2. 1 / a + 1 / b + 1 / c
  3. 1 / 5 / x ^ 2 + 1 / 7 / x ^ 3
  4. 5 / 4 / x - 5 / 6 / x ^ 3


Algebra Coach Exercise on factoring a difference of squares.
Factor each of the following expressions. To do this drag-and-drop each of these problems into the Algebra Coach and click the Factor button.
  1. y ^ 2 - 25
  2. - x ^ 2 + 9
  3. 9 x ^ 2 - 4
  4. m ^ 4 - n ^ 4
  5. 121 a ^ 4 - 16


Algebra Coach Exercise on factoring a sum of squares over the complex numbers.
Factor each of the following expressions. To do this drag-and-drop each of these problems into the Algebra Coach and click the Factor button.
Required Options settings: the complex number option must be turned on.
  1. a ^ 2 + 25
  2. - b ^ 2 - 9
  3. 9 c ^ 2 + 4
  4. 121 a ^ 4 + 16
  5. b ^ 4 + a ^ 2 c ^ 2


Algebra Coach Exercise on factoring perfect square quadratic trinomials.
Factor each of the following expressions. To do this drag-and-drop each of these problems into the Algebra Coach and click the Factor button.
  1. x ^ 2 - 8 x + 16
  2. 16 x ^ 2 - 8 x + 1
  3. 20 x ^ 2 + 60 x + 45
  4. 4 a ^ 2 - 20 a b + 25 b ^ 2
  5. 4 b ^ 2 - 4 b c + c ^ 2


Algebra Coach Exercise on factoring quadratic trinomials when a = 1.
Factor each of the following expressions. To do this drag-and-drop each of these problems into the Algebra Coach and click the Factor button.
  1. x ^ 2 + 10 x + 16
  2. x ^ 2 - 8 x + 15
  3. x ^ 2 + 12 x - 45
  4. a ^ 2 - 5 a - 24
  5. b ^ 2 + 13 b + 30


Algebra Coach Exercise on factoring quadratic trinomials when a ≠ 1.
Factor each of the following expressions. To do this drag-and-drop each of these problems into the Algebra Coach and click the Factor button.
  1. 4 x ^ 2 - 13 x + 3
  2. 5 x ^ 2 - 8 x + 3
  3. 8 x ^ 2 - 18 x + 10
  4. 20 a ^ 2 - 70 a + 30
  5. 16 b ^ 2 + 24 b - 16


Algebra Coach Exercise on factoring by grouping.
Factor each of the following expressions. To do this drag-and-drop each of these problems into the Algebra Coach and click the Factor button.
  1. x^3 + a x^2 + a b + b x
  2. -3 x^2 + x^2 y^2 - 2 y^2 + 6
  3. 2 c + c x + 2 d + d x
  4. 4 c + 2 c x - 2 d - d x


Algebra Coach Exercise on factoring a sum or difference of cubes.
Factor each of the following expressions. To do this drag-and-drop each of these problems into the Algebra Coach and click the Factor button.
  1. x^3 + 64
  2. 8 x^3 + y^3
  3. 2 x^3 - 16
  4. 8 x^3 - 64 y^3
  5. x^3 y^3 + 1
  6. y^9 + z^6