Section 3.1
Section 3.2
Section 3.3
Naming Polynomials
Random
200
Simplify
(15x4 + 13x2 - 9x + 13) + (8x4 + 4x2 - 7x + 35).
23x4 + 17x2 - 16x + 48
200
Find the degree.
(x4 - 1)3(x5 - x - 3)2
22
Remember when multiplying we add the exponents.
200
Divide using any method of your choice.
3x3 +5x2 - 11x + 3 ÷ x + 3.
3x2 - 4x + 1
200
Name this polynomial by its degree and number of terms.
10x
Linear Monomial
200
Describe the difference between even and odd multiplicity.
Zero with even multiplicity, graph touches the x-axis.
Zero with odd multiplicity, graph crosses through x-axis.
400
Simplify
(8x4 - 12x + 3) - (17x3 - 8x4 + 10x - 15)
-17x3 - 22x - 12
400
Graph y = x3 - 4x2 + 4x - 5. Identify the local extrema and write them as order pairs.
Local minimum (1.999, -5)
Local maximum (.667, -3.81)
400
Divide using any method of your choice.
2x3 + 5x2 + 7x +5 ÷ x + 2
2x2 + x + 5 - 5/x + 2
400
Name this polynomial by its degree and number of terms.
4x5 + 3x - 17
Quintic Trinomial.
400
Describe the end behaviors of a graph with an odd degree.
Odd degree and positive leading coefficient, graph starts low and finishes high.
Odd degree and negative leading coefficient, graph starts high and finishes low.
600
Simplify
(3x2 + 5x)(5x3 + 3x - 2)
15x5 + 25x4 +9x3 +9x2 -10x
600
Identify the x-intercepts and their multiplicities. Describe the graph at each zero.
f(x) = x2(x - 4)3(x + 2)
Zeros: 0 (multiplicity of 2), 4 (multiplicity of 3), -2.
x = 0, touch
x = 4 cross
x = -2 cross
600
Divide using any method of your choice.
x4 - 17x2 +4x - 2 ÷ x2 + 4x -1
x2 - 4x - 2/x2 + 4x -1
600
Name this polynomial by its degree and number of terms.
9x7 + 5x4 + 4x2 - 8x
Heptic Quadrinomial
600
Describe the end behavior of the following equation. How many turning points will there be?
f(x) = -2x8 + 4x - 6
Degree = 8
Negative leading coefficient
Both ends point down.
Number of turning points = 7
800
Simplify
(x-3)(x+3)(x2 + 9)
x4 - 81
800
Write the equation in standard from with the given zeros.
0 (multiplicity of 3), 2 (multiplicity of 1), -5 (multiplicity of 2)
x6 +8x5 +5x4 - 50x3
800
Divide using any method of your choice.
8x2 + 2x - 4 ÷ 2x -1
4x + 3 + 1/2x - 1
800
Name this polynomial by its degree and number of terms.
3x3 + 2x - 1
Cubic Trinomial
800
Based on the graph below, what are the zeros, describe their multiplicities, is the degree even or odd, is the leading coefficient negative or positive?
Zeros: -3 odd, -1 even, 2 even
Degree = even
Leading coefficient = positive
1000
Simplify 4xy3(2x2y - 5xy4 + 6xy + 9x2y)
44x3y4 - 20x2y5 + 24x2y4
1000
Write the equation for a polynomial in standard form with the given zeros.
-1/3 (multiplicity of 2), 3/4 (multiplicity of 1)
36x3 - 3x2 -14x - 3
1000
Divide using any method of your choice.
-6x4 + 3x3 + 7x2 - 13x + 16 ÷ -2x2 + 5
2x2 - x + 4 - 8x - 4/-2x2 + 5
1000
Name this polynomial by its degree and number of terms.
4x8 - 10
Octic Binomial
1000
Write a polynomial in standard form with zeros at 4 (multiplicity of 2) and 3 (multiplicity of 1) that also goes through the point (2, -20).
f(x) = 5x3 - 55x2 + 200x - 240