### 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.
- 10 x - 5 y
- 4 x ^ 3 + 3 x ^ 2
- x ^ 4 + 3 x ^ 3 - x ^ 2
- 2 (a + b) ^ 4 + 5 (a + b) ^ 2
- 5 x y ^ 3 - 15 x ^ 3 y + 10 x y
- 4 x + 8 x y + 12 x z
- 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 / x ^ 3 + 1 / x ^ 5
- 1 / a + 1 / b + 1 / c
- 1 / 5 / x ^ 2 + 1 / 7 / x ^ 3
- 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.
- y ^ 2 - 25
- - x ^ 2 + 9
- 9 x ^ 2 - 4
- m ^ 4 - n ^ 4
- 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.
- a ^ 2 + 25
- - b ^ 2 - 9
- 9 c ^ 2 + 4
- 121 a ^ 4 + 16
- 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.
- x ^ 2 - 8 x + 16
- 16 x ^ 2 - 8 x + 1
- 20 x ^ 2 + 60 x + 45
- 4 a ^ 2 - 20 a b + 25 b ^ 2
- 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.
- x ^ 2 + 10 x + 16
- x ^ 2 - 8 x + 15
- x ^ 2 + 12 x - 45
- a ^ 2 - 5 a - 24
- 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.
- 4 x ^ 2 - 13 x + 3
- 5 x ^ 2 - 8 x + 3
- 8 x ^ 2 - 18 x + 10
- 20 a ^ 2 - 70 a + 30
- 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.
- x^3 + a x^2 + a b + b x
- -3 x^2 + x^2 y^2 - 2 y^2 + 6
- 2 c + c x + 2 d + d x
- 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.
- x^3 + 64
- 8 x^3 + y^3
- 2 x^3 - 16
- 8 x^3 - 64 y^3
- x^3 y^3 + 1
- y^9 + z^6