Polynomial Properties & Operations (3.1 & 3.2)
Dividing & Factoring Polynomials (3.3 & 3.4)
Finding Roots of Polynomials (3.5 & 3.6)
Graphs of Polynomials & Transforming Polynomial Functions (3.7 & 3.8)
Curve Fitting & Misc. (3.9)
100
Rewrite each polynomial in standard form. Then identify the leading coefficient, degree, and number of terms. Name the polynomial.
1-11x+9x^2
standard form:
9x^2-11x+1
leading coefficient: 9
degree: 2
number of terms: 3
name: quadratic trinomial
100
Divide.
(x^3-5x^2+2x-7)/(x+2)
x^2-7x+16-39/(x+2)
100
Identify the REAL roots of the equation. (including multiplicities)
x^3-5x^2+8x-4=0
x=1,2 (M of 2)
100
Identify the leading coefficient, degree, and end behavior.
f(x)=-3x^6+9x^3-2x-9
leading coefficient: -3
degree: 6
end behavior:
x->- infty, f(x)->- infty
x-> infty, f(x)->- infty
100
What do people typically put on the top of a Christmas tree?
An angel
200
Add.
(6x^2+7x-2)+(1-5x^3+3x)
-5x^3+6x^2+10x-1
200
Factor.
x^3-x^2-16x+16
(x-1)(x-4)(x+4)
200
Identify the REAL roots of the equation.
x^4-12x^2+27=0
x=-3, 3,+-sqrt3
200
Graph the function using the zeros, y-intercept, and by plugging in x-values.
f(x)=x^4-10x^2+9
200
Determine what degree best fits the following function.
cubic because the third difference are constant
300
Subtract.
(5x-2x^2)-(4x^2+6x-9)
-6x^2-x+9
300
(8x^4+6x^2-2x+4)/(2x-1)
4x^3+2x^2+4x+1+5/(2x-1)
300
Find ALL roots by factoring.
x^3-x^2+4x-4=0
x=1, +-2i
300
Write a function that transforms
f(x)=x^4-6x^2-4
by stretching vertically by a factor of 2 and moving 2 units up.
g(x)=2x^4-12x^2-6
300
What popular Christmas song was actually written for Thanksgiving?
"Jingle Bells"
400
Multiply.
ab^2(a^2-a+ab)
a^3b^2-a^2b^2+a^2b^3
400
Determine whether (x-1) is a factor of the polynomial
P(x)=4x^4-5x^2+3x-2
Yes, the remainder is zero.
400
Write the equation if the graph bounces off the x-axis at 4, bends around the x-axis at -6, and goes straight through the x-axis at 1. (Leave in factored form)
Then sketch a graph.
y=(x-4)^2(x+6)^3(x-1)
400
Write a function that transforms
f(x)=x^4-6x^2-4
by moving 2 units down and reflecting across the x-axis.
g(x)=-x^4+6x^2+6
400
The table shows the attendance for a new movie theater over five days. Write a polynomial function for the data.
f(x)~~-6.67x^4+80x^3-328.33x^2+575x-72
500
Find the product.
(2x+1)^4
16x^4+32x^3+24x^2+8x+1
500
Factor.
16x^3-2
2(2x-1)(4x^2+2x+1)
500
Write the simplest polynomial function in factored form with the given roots.
sqrt(3), 2i
(x^2-3)(x^2+4)
500
Find the local minima and maxima of the function (round to the tenths)
f(x)=-x^3+5x^2+x-5
minimum: -5.1
maximum: 16.9
500
What are Miss Ely's top two favorite Christmas movies?
Elf & National Lampoon's Christmas Vacation