Algebra §

• Algebra is based on Abstract ideas to explain things that are intangible like economics, norms, theories…

Polynomial §

• Polynomial (many names/terms): a sum of a finite number of terms. Conditions to be a polynomial are:
  • Variable: (ex: $x,y,a,b$) letters used to represent an unknown number
  • Term: each item in the formula ($+3x^2$, $-8x^1$, $+7x^0$)
  • Exponent: the power of the x (2, 1, 0)
    • All term’s exponent must be positive to be a polynomial
  • Coefficient: the multiplier of the X (+3, -8, +7)
    • All coefficients must be an integer to be polynomial (not fractions: $x^{\frac{1}{2}}$ or an integer: $x^{\sqrt{a}}$)

[!Formula for polynomials]

$$\text{Formula:}\pm A{x}^{+n}\pm B{x}^{+o}\pm C{x}^{+p}\pm ...$$ $$\text{Ex:}+3x^2-8x^1+7x^0$$

• Types of Polynomials
  • Monomial: 1 term (ex: $6x^0$)
  • Binomial: 2 terms (ex: $9a^2-5$)
  • Trinomial: 3 terms(ex: $+3x^2-8x^1+7x^0$)
• Degrees of polynomial: is the highest coefficient seen in all the terms of the polynomial
  • We can say $3y^3+5y$ is “A third degree binomial”
• Normally we write polynomials in the standard form: where degrees count down from left to right, highest to lowest
  • $10x^7+15x^3-9x^2+9$

Average Rate of Change §

• Is a type of exercise that asks for the average rate of change in a function $f(x)$ over the interval of $[n,m]$
  • It’s represented by $\frac{\Delta f}{\Delta x}=\frac{y(x_f)-y(x_i)}{x_f-x_i}$

Example

$x$	$y=f(x)$
-2	0
3	15
$\Delta x=5$	$\Delta y=15$
$\frac{\Delta y}{\Delta x}=\frac{15}{5}=3$