Key Features of
Polynomial Functions
Polynomial Functions
What is the domain of all polynomial functions?
(-oo,oo)
"All real numbers"
Determine the degree of the polynomial function:
f(x)=8x^3-12x^4+9x
4
Simplify the following expression:
3x^7+10x^7
13x^7
Determine the product:
(8n^7)(7n^8)
56n^15
Determine the quotient:
(-60n^14)/(15n^5)
-4n^9
Find the end behavior for the polynomial function f(x)=-8x6.
x->-oo, f(x)->
x->oo, f(x)->
x->-oo, f(x)->-oo
x->oo, f(x)->-oo
Determine the leading coefficient of the polynomial function:
g(x)=-7x^6-3x+x^4-x^8
-1
Determine the sum of the two polynomials:
(3c^2-8c+4)+(5c^2-c+1)
8c^2-9c+5
Multiply:
-2p(3p^3-p^2+5p-6)
-6p^4+2p^3-10p^2+12p
Use factoring to determine the quotient:
(x^2+6x-40)/(x-4)
x+10
Identify the x- and y- intercepts of the polynomial function f(x)=x3-3x2-4x.
x-intercepts: (-1,0), (0,0), and (4,0)
y-intercept: (0,0)
Rewrite h(x) in standard form:
h(x)=9x-5x^3-x^2+18+2x^4
h(x)=2x^4-5x^3-x^2+9x+18
Determine the sum of the two polynomials:
(12x-8x^2+3x^3-10)+(6x^3-15x^2-22x-15)
9x^3-23x^2-10x-25
Expand and simplify the following expression:
(3x-2)^2
9x^2-12x+4
Determine the quotient:
(25x^8y^7-15x^12y^6+5x^9y^4)-:(5x^2y^3)
5x^6y^4-3x^10y^3+x^7y
What is the difference between the extrema and the zeros of a polynomial function?
The extrema of a polynomial function are its minimum and maximum values (i.e., the "low points" and the "high points" on a graph). The zeros of a polynomial function are its solutions (i.e., roots) that are found where the graph crosses the x-axis.
Find the value of f(x) when x=1:
f(x)=2x^3-3x^2-4x+12
7
Determine the difference of the two polynomials:
(6a^4-7a^3+a^2-1)-(a^4-3a^3+a^2+2a)
5a^4-4a^3-2a-1
Multiply:
(x+2)(x-3)(3x+4)
3x^3+x^2-22x-24
Use synthetic division to determine the quotient:
(-8x^3+40x^2-37x+30)-:(x-4)
-8x^2+8x-5, r10
or
-8x^2+8x-5+10/(x-4)
What is the range of the polynomial function f(x) = x8 - 3?
[-3,oo)
"Everything greater than or equal to -3"
Given the prefix "poly-" and the base word "-nomial," what does the word "polynomial" mean? Your response should be exactly 2 words.
"Many terms"
Determine the difference of the two polynomials:
(15x^3-12x^4-16-x^2+10x^5-9x)-(5-18x^2+5x^5+7x^4-10x)
5x^5-19x^4+15x^3+17x^2+x-21
Multiply:
(2y^2-6y+3)(4y^2-y+1)
8y^4-26y^3+20y^2-9y+3
Use long division to determine the quotient:
(3x^3-5x^2+10x-3)-:(3x+1)
x^2-2x+4-7/(3x+1)