The Fundamental Theorem of Algebra (Lesson 5-6)
2 x 3 + 5 x 2 + 9 = 0 2 x cubed , plus 5 , x squared , plus 9 equals 0  has factored form ( x + 3 ) ( 2 x 2 − x + 3 ) = 0 . open x plus 3 close open 2 , x squared , minus x plus 3 close equals 0 .  It has 3 roots or solutions, x = − 2 , x equals negative 2 comma
x = 1 4 − 23 4 i , x equals , 1 fourth , minus , fraction square root of 23 , over 4 end fraction , i . comma  and x = 1 4 + 23 4 i . x equals , 1 fourth , plus , fraction square root of 23 , over 4 end fraction , i . .

1. Conjugate Root Theorem
2. Fundamental Theorem of Algebra
3. Rational Root Theorem
4. Remainder Theorem

1. determines P ( a ) p open eh close  by dividing the polynomial by x − a x minus eh
2. the degree equals the number of roots
3. minimizes guessing fraction and integer solutions
4. complex numbers as roots come in pairs