Algebra : Simplifying Expressions and Solving Equations

1. Divide, then write the result as a division statement.
a) (x3-3x2+5x-4)/(x-2)
X not equal to 2
___________
x-2)x3-3x2+5x-4
x3-2x2
-x2+5x
-x2+2x
3x-4
3x

b) (x3-3x-2)/(x+3)

2. Use the Remainder Theorem to determine the remainders ( do not divide).

Expressions are simplified and equations are solved. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

30. Assume that Joe take 6 hours working alone and Sam takes 8 hours working alone, how long does it take the, to do it together?
54. (1 +3i) (2-5i)
64. i(3-4i) (6+4i)
84. 14 + 5i divided by 3 +2i
94. 5 divided by 9i

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Simplifying the folllowing expressions
3. (sqrt(x^3) + 3x)^2
5. The sixth term in the expansion of (2x - y)^8 is
6. Factor completely: x^4 - 3x^3 + 8x - 24
10. Rationalize the denominator: (x - 2)/(x - sqrt(x + 2))
11. solve for x: (3x + 4)/2 = 1 - x/3
12. solve for x(x - 3)

Chapter 2 of Elementary and Intermediate Algebra. I do not understand the questions below:
1.What is the difference between an equation and an expression? How does knowing how to simplify an expression help with solving an equation?
2.When is it all right to cross-multiply when solving an inequality, and what are the rul

1. Simplify: (-5a^3b^2)^4 a^12b^5/b^-7
2. let f(x)=3x^2 and g(x)=x-4
-Find the composite function (f o g)(x) and simplify
-Find (f o g)(-1)
3. Find the exact solutions and simplify as much as possible 4x^2+5=4x

How does the knowledge of simplifying an expression help you, personally, to solve an equation efficiently? Give an example from your life in how knowing the reason why helped you with the process of solving a difficult situation or problem.