Polynomial Graph Features
Operations with Polynomials
Factoring
Dividing & Zeros of Polynomials
Exp./Log Equations
100
Describe the end behavior of the graph:
As x -> -∞, f(x)-> -∞
As x->∞,f(x)->+∞
100
Simplify
x^2(x+7)
x^3+7x^2
100
Fill in the missing signs (+/-) to the following polynomial identity:
100
Using synthetic division divide x^3+7x^2+10x-6 by x+3.
100
Solve for x. Round your answer to the nearest hundredth:
60 times3^x=55
xapprox-2.18
200
What is the degree of the polynomial? Is it an odd, even OR neither function?
f(x)=5x^4-2x^2+7?
4, even.
200
Simplify
(x^3+4x^2-x)-(3x^3-2x^2-x-9)
-2x^3+6x^2+9
200
Factor:
x^4+x^2-6
(x^2+3)(x^2-2)
200
Given: (x-3)^2(x+1)^3
What are the zeros, their multiplicity and describe if the graph bounces or crosses at the zero.
x=3
Multiplicity: 2 | Bounces (even multiplicity/exponent)
x=-1
Multiplicity: 3 | Crosses (odd multiplicity/exponent)
200
Eva invested $31,000 in an account paying an interest rate of 3.8% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest cent, would be in the account after 20 years?
A≈$66,286.56
300
What can you say about the degree and sign of the leading coefficient of the graph below? Is the function odd, even OR neither?
Odd degree, negative leading coefficient, neither.
300
Multiply
(3x-2)(x+7)
3x^2+19x-14
300
Factor completely:
x^4-16
Difference of Squares
(x^2-4)(x^2+4)
(x-2)(x+2)(x-2i)(x+2i)
300
Is (x-1) a factor of f(x)=x3+7x2+4x-12?
Yes.
300
Solve for x:
32^(x-5)=8^(2x+3)
x=-34
400
Write a polynomial in factored form that has 3 roots.
Answers may vary.
400
Expand:
(2x-3)^2
(2x-3)(2x-3)
4x^2-12x+9
400
Factor:
27x^3+8
400
Using a graph, identify the number of real and imaginary zeros f(x) has.
f(x)=2x^4+5x^3+3x^2+15x-9
2 real, 2 imaginary
400
Solve for x:
log_2(2x)+log_2(x)=5
x=4
500
A graph touches at x = –1 and crosses at x = 2 and 4. Write one possible function.
Example: f(x)=(x+1)^2(x-2)^3(x-4)
500
Multiply
(x^2+6x-7)(2x+2)
2x^3+14x^2-2x-14
500
Solve algebraically:
f(x)=x^3-64
x=4,-2+-2isqrt3
500
If f(x)=x3+2x2+x+2 and x+2 is a factor of f(x), then find all of the zeros of f(x) algebraically.
x=-2,+-i
500
Aubree invested $16,000 in an account paying an interest rate of 5.6% compounded continuously. Assuming no deposits or withdrawals are made, how long would it take, to the nearest tenth of a year, for the value of the account to reach $45,600?
t≈ 18.7