Polynomial Functions
1. y=-x4+12, quartic binomial, down and down
2. y=x4-3x3+3x2+10, quartic polynomial of four terms, up and up
3. If n is even there are an odd number of turning points, if n is odd there are an even number of turning points
Polynomials-Linear-Factors-Zeroes
1. f(x)=x3-3x2-6x+8
2. 2 (multiplicity 2), -2 (multiplicity 2)
3. relative maximum: (-0.8441, 9.3023), relative minimum: (0.7108, -0.0964), zeroes: x=-1.6180, x=0.6180, x=0.8
Solving Polynomials
1. -1/2
2. 2.3949
Transforming Polynomials
1) y = -(x - 2 )3 + 1
2) y = 6(x + 3)3
Polynomial Modeling
1) 3.5x2 – 4.5x + 5
2) Cubic is the best fit since R2 = 1
3) Y = -5.8667x3 + 120.5333x2 -629.2667X + 1421 ; =1097 is the population
Binomial Theorem
1. 105
2. b4+8b3+24b2+32b+16
3. 6a2c2
Theorem About Roots
1. 2, -1/5, 1/3
2. -√2 and 1-i
3. X3+4x2+4x+16=0
4. one negative real root, one sign change from - to +
Polynomial Division
1. quotient= 4x+3, remainder=-31
2. no
3. quotient= X2-16x+83, remainder=-220
4. L=(x+8) in, w=(x+5) in, h=(x-6)in
Fundamental Theorem
