Vocabulary
Name 2 methods to solve a quadratic equation
Factoring, Square Roots, Quadratic Formula, Completing the Square, Graphing
Describe the end behavior P(x)= 2x3-4x+1
What is:
as x -> infinity, P(x) -> infinity
as x - >- infinity, P(x) -> -infinity
This is a form of division we use as a shortcut
Synthetic division
Find the roots by factoring x2 + 14 = 9x
x2 - 9x + 14 = 0
(x - 7)(x - 2)
What are: 7, 2
Find all the rational roots of the polynomial equation. 4x3 - 13x2 + 11x - 2 = 0
What are: 1/4, 1, 2
A solution to a polynomial function.
What is a ZERO or ROOT?
Determine the end behavior for the function P(x)= x4-2x2+2
What is:
as x -> infinity, P(x) -> infinity
as x -> -infinity, P(x) -> infinity
Multiply (2x - 4)(x + 1)2
What is 2x3-6x-4
Solve by factoring: 3y3 + 36y2 = 3y4
-3y4 + 3y3 + 36y2 = 0
-3y2( y2 - 1y - 12)
-3y2(y - 4)(y + 3)
What is y = {0, -3, 4}
Find all zeros of each polynomial function. B(x) = x3 - 4x2 - 3x + 12
What are: 4, and +- sqrt(3)
A factor that occurs more than once when a function is factored out.
What is MULTIPLICITY?
Find the y-intercept for the function P(x)= -x4-3x3+3x+3
y intercept is when x = 0
P(0)=−(0)4−3(0)3+3(0)+3
What is (0, 3)
Use synthetic division to divide: (x5+6x3-5x4+5x-15) ÷(x-3)
x5 - 5x4+6x3 + 5x-15
3 | 1 5 6 0 5 -15
3 6 0 0 +15
1 2 0 0 5 0
What is x4- 2x3+ 5
Use a graph, synthetic division and factoring to find all the roots of the equation: x3 + 3x2 = 27 + 9x
x3 + 3x2 - 9x - 27 = 0
x2 (x + 3) - 9(x + 3)
(x2 - 9)(x + 3) --> x2 = 9 --> x = +/-3
Factoring (x+3)2(x−3)
What are: 3 and -3
Write a polynomial function, P, in factored form by using the given information. P is of degree 3; zeros: -1, 2, 4
What is P(x) = (x + 1)(x - 2)(x - 4)
When describing what the graph of a polynomial is doing on the left and right side, you are describing the polynomial's ...
What is END BEHAVIOR?
Find the x-intercepts of the polynomial function P(x)= (2x + 1)(x - 3)(4x + 5)2
(2x+1)(x−3)(4x+5)2=0
x=−1/2,x=3, x=−5/4
What is (-1/2, 0), (3, 0), (-5/4, 0)
Use synthetic division to divide: (x2+1/2x - 3/16)÷ (x+ 3/4)
What is (x - 1/4)
Solve the polynomial by factoring. Approximate any irrational zeros. f(x) = x2 + 12x3 - 3x
What are: 0, -0.54, 0.46
Find all zeros of the polynomial function. H(x) = x4 + 16x - x2 + 4x3 - 20
What are: -5, 1, + or - 2i
This states that the number of roots of a polynomial function can be determined by its degree
What is the fundamental theorem of algebra
Tell where the x-intercepts are and whether the graph crosses or touches at each x-intercept for the polynomial function P(x)= (2x + 3)(x2 - 16x + 64)
(2x + 3) x = -3/2 Linear function x crosses
x2−16x+64 is perfect sq (x - 8)2, x = 8 x2 touches
What is Crosses at (-3/2, 0) Touches x2 fn at (8, 0)
Factor by grouping: 2x3 - 5x2 + 10x - 25
x2 (2x -5) + 5(2x -5)
What is (x2 + 5)(2x - 5)
Solve the polynomial by factoring. Approximate any irrational zeros. f(x) = x2 - 5x3 + 3x
What are: 0, -0.68, -0.88
Write a polynomial function, P, in factored form. P is of degree 4; zeros: 1 (multiplicity 2), 2 (multiplicity 2)
What is P(x) = (x - 1)^2(x - 2)^2