Algebra Concepts for Review

Algebra Simplification and Operations

  • Expression Simplification

    • Simplify the following expression:
      x2+7x+10x2+2x−8\frac{x²+7x+10}{x²+2x-8}
    • Result: Requires factoring and canceling common terms.

  • Factoring Polynomials

    • Example:
    • x2−9x² - 9 can be factored as (x+3)(x−3)(x + 3)(x - 3).

  • Further Simplification

    • Reduce the expression (2x2−9x+5x+6)(\frac{2x² - 9}{x + 5x + 6}) to its simplest form through factoring.

Solving Equations

  • Arithmetic Operations

    • Solve the following:

    1. 2x2+3x−10=02x² + 3x - 10 = 0

      • Use the quadratic formula: x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b² - 4ac}}{2a}.

    2. x2+8x+15=0x² + 8x + 15 = 0

      • Factor into: (x+3)(x+5)=0(x + 3)(x + 5) = 0.

  • Complex Equations

    • Operations to handle equations like:
      x−162x2+9x+4\frac{x-16}{2x² + 9x + 4} with division of polynomials.

Systems of Equations

  • Graphing Method

    • System:
    1. y=2x−8y = 2x - 8
    2. 3x+y=63x + y = 6
    • Find the intersection by graphing both equations on the same set of axes.

  • Substitution Method

    • Solve this system:
    1. x+5y=10x + 5y = 10
    2. 3x−2y=83x - 2y = 8
    • Express one variable in terms of another and substitute.

  • Elimination Method

    • Solve the following:
    1. 2x−5y=142x - 5y = 14
    2. 3x+3y=53x + 3y = 5
    • Involve adding or subtracting equations to eliminate one variable.