Polynomial Functions
Find the end behavior of -7x3 + 8x2 + x.
as x approaches negative infinity; f(x) approaches positive infinity
as x approaches positive infinity; f(x) approaches negative infinity
Factor: x3 + 7x2 + 10x
x(x + 5)(x + 2)
Solve x3 + 13x = 10x2
x = 0, x = (5 + 2square root of 3)/2 x = (5 - 2square root of 3)/2
(x3 + 3x2 - x - 3) / (x -1)
x2 + 4x + 3
Classify 3 + 12x4 by degree.
Quartic
Factor: x3 - 7x2 +18x
x(x - 9)(x + 2)
Find the roots: y = x (x + 1)3
x = 0, x = i, x = i, x = i
Solve 12x3 = 60x2 + 75x
x = 0 x = (5 + 5square root of 2)/2 x = (5 - 5square root of 2)/2
(x3 - 4x2 + 6x - 4) / (x -2)
x2 - 2x + 2
Factor: x3 - 36x
x(x - 6)(x + 6)
Find the zeros and state the multiplicity of y = (2x + 3)(x - 1)2
x = -3/2, multiplicity of 1 x = 1, multiplicity of 2
Solve 27 = -x4 - 12x2
x = 3i x = -3i x = i square root of 3 x = -i square root of 3
(x3 + 27) / (x + 3)
x2 - 3x + 9
Write (2a - 5)(a2 - 1) in standard form. Then classify by degree and number of terms.
2a3 - 5a2 - 2a + 5 Cubic Polynomial of 4 terms
Factor: 9x3 + 6x2 - 3x
3x(x + 1)(3x - 1)
Solve 125x3 + 216 = 0
x = -6/5 x = (3 + 3i square root of 3)/5 x = (3 - 3i square root of 3)/5
Find P(a). P(x) = x3 + 4x2 - 8x - 6; a = -2
18
Give an example of a Binomial with a degree of 7, a lead coefficient -4 and a constant of 2.
-4x7+2
Given x = -2, 0, 1, write the polynomial equation.
x3 + x2 - 2x = 0
Find the zeros and state the multiplicity of y = 2x3 + x2 - x.
x = 0, multiplicity of 1 x = -1, multiplicity of 1 x = 1/2, multiplicity of 1
Solve x3 + 1 = x2 + x
x = 1 x = -1
Factor Completely: (x3 + 2x2 - 5x - 6) / (x + 1)
(x + 1)(x + 3)(x - 2)