Graphing Polynomials
Adding and Subtracting Polynomials
Multiplying Polynomials
Factored Form of Polynomials
Miscellaneous
100
What is the degree of the polynomial
2x^3 +x^5 -x^4 +7 ?
Degree = 5
100
This is the name for any terms that have the same variable and exponent.
"Like Terms"
100
The function f(x) is defined as f(x)=(x+2)(x-4)(x+8)^2 . The binomial (x-4) is considered a __________ of the polynomial.
"Factor"
100
A "zero" is the value of
x when
y=?
y=0
100
This is the special name we give to a polynomial that has 2 terms.
"Binomial"
200
What is the leading coefficient of the polynomial
4x^4 + 3x^3 +2x^2 +x + 1 ?
Leading Coefficient = 4
200
What is (2x^3 + 3x^2 +4) + (6x^3 -x^2 -5x) ?
8x^3 +2x^2 -5x+4
200
Simplify the following expression and write the final answer in standard form (7x^2-4)(x^3+5)
7x^5 -4x^3 +35x^2 -20
200
What are the zeros for the quadratic polynomial below?
f(x)=(x-3)(3x+1)
Zeros: 3, -1/3
200
How would we classify a polynomial that has a degree of 3 and has 3 terms?
"Cubic Trinomial"
300
What is the end behavior of the polynomial -3x^3 +4 ?
x-> +infty, y-> -infty
x-> -infty, y-> +infty
300
What is (5x^3 - 2x^2 + 3) - (x^2 +2x+ 3) ?
5x^3 -3x^2 -2x
300
Multiply the following binomials:
(x-4)(x+4)(2x-3)
2x^3 -3x^2-32x+48
300
What is the equation for the graph below in factored form?
y=(x+1)(x-1)(x-2)^2
300
What is
(5p^2-3)+(2p^2-3p^3) ?
-3p^3+7p^2-3
400
A polynomial has the following end behavior:
x->+infty, y-> +infty
x->-infty, y->+infty
Describe the degree and the leading coefficient of the polynomial.
The degree is even.
The leading coefficient is positive.
400
Simplify (-9v^2-8u)+(-2uv-2u^2+v^2)+(-v^2+4uv)
-9v^2+2uv-8u-2u^2
400
Multiply the following polynomials and write the final answer in standard form:
(0.7-x^2)(x^3-2x^2+x)
-x^5 +2x^4 -0.3x^3 -1.4x^2+0.7x
400
Determine the zeros for the polynomial y = x^3 -8x^2+16x . State the multiplicity for any multiple zeros.
1. x=0, multiplicity 1
2. x=4, multiplicity 2
400
Determine the zeros for x^4-25x^2 and state the multiplicity of any multiple zeros.
1. 0, multiplicity of 2
2. 5, multiplicity of 1
3. -5, multiplicity of 1
500
Use a function table to estimate one of the two turning points for the function f(x)=x^3+2x^2-5x-6 . (Hint: both of the turning points are between -4 and +4)
1. between -3 and -2 (approx. -2.12)
2. between 1 and 2 (approx. 0.786)
500
The length of a rectangle is represented by 3x^3-2x^2+10x-4 , and the width is represented by -x^3+6x^2-x+8 . What is the perimeter of the rectangle?
Perimeter =
4x^3+8x^2+18x+8
500
The length of a rectangular speaker is three times its width. The height of the rectangular speaker is four more than the width. Write an expression for the volume, V, of the rectangular prism in terms of its width, w. Write your final answer in standard form.
V=3w^3+12w^2
500
A function has zeros at 1 and -1, each with multiplicity 1. The function also has a zero at -2 with multiplicity 2. Write the equation for this function in standard form.
x^4+4x^3+3x^2-4x-4
500
Write the equation for a polynomial function in factored form that has zeros at -2, 3, and 4 (which has a multiplicity of 2) and a y-intercept at 192.
y=-2(x+2)(x-3)(x-4)^2