Mathematics Class Notes
1. Algebra: Solving Linear Equations
• Definition: An equation of the form ax+b=0ax + b = 0 , where aa and bb are
constants.
• Steps to Solve:
o Isolate xx on one side.
o Solve for xx.
• Example: Solve 2x+5=92x + 5 = 9 : 2x=9−5=4⇒x=42=22x = 9 - 5 = 4 \quad
\Rightarrow \quad x = \frac{4}{2} = 2
2. Polynomials
• Definition: An expression of the form axn+bxn−1+⋯+kax^n + bx^{n-1} + \cdots
+ k, where a,b,ka, b, k are constants and nn is a non-negative integer.
• Operations:
o Addition: Combine like terms.
o Subtraction: Subtract like terms.
o Multiplication: Use distributive property.
o Factoring: Express as a product of simpler polynomials.
• Example: Factor x2−5x+6x^2 - 5x + 6
x2−5x+6=(x−2)(x−3)x^2 - 5x + 6 = (x - 2)(x - 3)
3. Quadratic Equations
• Form: ax2+bx+c=0ax^2 + bx + c = 0
• Methods:
o Factoring: If possible, factor the equation and solve.
o Quadratic Formula: x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 -
4ac}}{2a}
1. Algebra: Solving Linear Equations
• Definition: An equation of the form ax+b=0ax + b = 0 , where aa and bb are
constants.
• Steps to Solve:
o Isolate xx on one side.
o Solve for xx.
• Example: Solve 2x+5=92x + 5 = 9 : 2x=9−5=4⇒x=42=22x = 9 - 5 = 4 \quad
\Rightarrow \quad x = \frac{4}{2} = 2
2. Polynomials
• Definition: An expression of the form axn+bxn−1+⋯+kax^n + bx^{n-1} + \cdots
+ k, where a,b,ka, b, k are constants and nn is a non-negative integer.
• Operations:
o Addition: Combine like terms.
o Subtraction: Subtract like terms.
o Multiplication: Use distributive property.
o Factoring: Express as a product of simpler polynomials.
• Example: Factor x2−5x+6x^2 - 5x + 6
x2−5x+6=(x−2)(x−3)x^2 - 5x + 6 = (x - 2)(x - 3)
3. Quadratic Equations
• Form: ax2+bx+c=0ax^2 + bx + c = 0
• Methods:
o Factoring: If possible, factor the equation and solve.
o Quadratic Formula: x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 -
4ac}}{2a}
