Monomials and Polynomials
Classify the polynomial by degree and # of terms.
9x4-x2+2
What is a Quartic Trinomial?
The parent function of a cubic polynomial
What is
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Finish the statements:
If the multiplicity is ODD, the graph _____ at that zero
If the multiplicity is EVEN, the graph ____ at that zero
What is
Crosses
Bounces
Factor (check for GCF's)
72x4-2
What is
2(6x2-1)(6x2+1)
Divide
(x2+3x-43) / (x+8)
What is
x-5-(3/x+8)
Describe the two rules used to write polynomials in standard form
What is
Exponents in descending order
Variables in alphabetical order
Determine the end behavior pattern
f(x) = 4x4+6x3-x
What is
As x->∞ , f(x)->∞
As x->-∞ , f(x)->∞
Identify the zero's, their multiplicity, and the effects:
f(x)=(x+7)2(2x+1)(x-4)3
What is
x=-7, mult. 2, bounces
x=-1/2, mult. 1, crosses
x=4, mult. 3, crosses
Factor (check for GCF's)
(500a3+4)
What is
4(5a+1)(25a2-5a+1)
Divide
(2x2-16x+19) / (x-7)
What is
2x-2+(5/x-7)
Multiply
(2x+1)(4-9x)-2x(3x+11)
What is -24x2-23x+4?
Describe the end behavior
f(x) = .5x3+7
What is
As x->∞ , f(x)->∞
As x->-∞ , f(x)->-∞
Identify the zero's, their multiplicity, and the effects:
3x(x-9)(x+4)5
What is
x=0, mult. 1, crosses
x=9, mult. 1, crosses
x=-4, mult 5, crosses
Factor (check for GCF's)
x3+5x2-x-5
What is
(x-1)(x+1)(x+5)
Divide
(x3-17x+32) / (x+5)
What is
x2-5x+8 - (8/x+5)
Multiply
-3(a+5)(a-2)(a+8)
What is -3a3-33a2-42a+240?
Give the relative maximums and minimums of the following polynomial:
What is
Rel Max(s): (1.37,-.65)
Rel Min(s): (-.37,-5.85), (2,-1)
The graph of a polynomial function has zero's 5 (multiplicity 2), -2 (multiplicity 1), and 0 (multiplicity 3). Write a function in standard form that could represent this function
What is
x6-8x5+5x4+50x3
Factor (check for GCF's) AND Solve
x3+3x2-24x-72 = 0
What is
(x2-24)(x+3)
x = +-2 sqrt(6)
x = -3
Divide
(2x3-14x+10) / (x+3)
What is
2x2-6x+4- (2/x+3)
Divide
(30x3-12x2+9x) / (3x2)
What is 10x-4+(3/x)?
Give the increasing and decreasing intervals of the following polynomial function:
What is
Inc int: (0,2)
Dec int: (-∞, 0) and (2,∞)
Define what a zero is and give 2 other names for what they can be called/referred to as
Zero's = ____________ = ________________
What is
The point(s) at which the function intersects the x-axis
Zero's = Solutions = Roots
Factor (check for GCF's) AND Solve
2x3-5x2+40x-100 = 0
What is
(x2+20)(2x-5)
x = +-2i sqrt(5)
x = 5/2
Divide
(x4-7x2-32x-15) / (x-4)
What is
x3+4x2+9x+4+ (1/x-4)