alg & geo II : note guides

number classification

• complex numbers

  • imaginary numbers

  • real numbers

    • irrational numbers

    • rational numbers

      • integers

      • whole numbers

      • natural numbers

possibilities for a system of equations

• no solution (parallel lines) — inconsistent (no common solutions) — independent (different lines)

• one solution (crossing lines) — consistent (at least one common solution) — independent (different lines)

• infinite solutions (overlapping lines) — consistent (at least one common solution) — dependent (same line)

uniform motion types

• equal distance

  • D1=D2

• given total distance

  • D1+D2=TOTAL

• given difference of distances

  • D1+GIVEN=D2

• two distances given

  • D1=GIVEN

  • D2=GIVEN

guide to factoring polynomials

1. put the polynomial in descending order

2. “factor out” anything you can

3. consider—do you have a SPECIAL CASE?

   1. difference of two squares: (A+B)(A-B)=A²-B²

   2. square of a sum:

      \left(A+B\right)^2=A^2+2AB+B^2

   3. square of a difference: \left(A-B\right)^2=A^2-2AB+B^2

otherwise:

1. does it have 4 terms?

2. if yes, factor by grouping

   1. 2x^3+6x^2+5x+10

otherwise:

1. is it a quadratic trinomial?

   1. ax^2+bx+c

2. if a is 1, then find the factors of C that add up to B

3. if a is anything but 1, find the factors of A times C that add up to B

4. then replace the middle term with those factors, factor by grouping