Polynomials and Factoring
Which polynomials have (x+1) as a factor? Name them all.
A. x2 - 1
B. x2 + 1
C. x3 - 1
D. x3 + 1
E. x4 - 1
A, D and E
Simplify
(x^2+2x-3)/(x^3-x^2)
(x+3)/(x(x+1))
Rewrite this logarithmic equation as an exponential equation and solve
log4x = -3
4(-3)= x
1/64=x
4 students want to know how many hours of sleep on average their fellow students get daily. They each decide to collect this data in different ways. Which way provides less bias?
Ava: Asked all of the students on her lacrose team.
Ben: Sent a message to all of his phone contacts.
Cylas: Asked two random people at each table in the lunch room.
Dani: Put all classroom numbers on pieces of paper and randomly selected 10 of them. She then went to those classrooms and the teachers allowed her to survey the students in those classrooms.
Dani's method would allow for less bias.
f(x) = 4(x-2)2+3
g(x) is a transformation of f(x). It represents a translation by 4 units to the right and 2 units up.
1. Write an equation for g(x).
2. What are the vertices of both of these functions?
1. g(x) = 4(x-6)2 + 5
2. f(x)'s vertex is (2, 3) and g(x)'s vertex is (6, 5)
Find the product:
(x - i)(x + i)(x - 2i)(x +2i)
x4 + 5x2 +4
Find the sum
1/(x-2)+1/(x+5)
(2x+3)/((x-2)(x+5))
Which of the following expressions are equivalent 36x. Name them all.
A. 62x
B. (1/6)-2x
C. (4x)(9x)
D. (72(1/2)x)(18(1/2)x)
E. 367x/366x
All of them
A total of 500 students took the ACT test at Hickman in 2024. The average composite score was 19.6 and the standard deviation was 5.9. If the scores were normally distributed,how many students had scores that fell between 13.7 and 25.5?
340
f(x) = x2
g(x) = -2(x+1)2 -3
What transformations would you have to complete on f(x) to arrive at g(x)?
left 1, down -3, vertical stretch by a factor of 2, x-axis reflection
What is the LCM of these three polynomials?
x2 + x - 6
x2 + 11x + 24
2x2 + 17x + 8
(x + 3)(x - 2)(x + 8)(2x + 1)
Find the quotient
(x^2+2x-8)/(x^2+x-6) divide (x^4-256)/(x^3+27)
(x^2-3x+9)/((x-4)(x^2+16))
Simplify the expression.
sqrt(162x^5y^6z^7)
9x^2y^3z^3sqrt(2xz)
What amount of money would be in each of the accounts below after 5 years?
A. $500 compounded annually at 7%
B. $600 compounded quarterly at 4%
C. $550 compounded monthy at 5.5%
D. $575 compounded continuously at 4.75%
A. $701.28
B. $732.11
C. $723.64
D. $729.14
Find the inverse of the function below:
f(x) = (2x+1)/3
f^-1(x)=(3x-1)/2
What are the x-intercepts and end behavior of the polynomial p(x) = x3 + 5x2 - 4x -20
(-2, 0) (2, 0) and (-5, 0)
As x->infinity, y->infinity
As x->negative infinity, y->negative infinity
Identify any vertical asymptotes and/or holes for the function
f(x)=(x^2+10x+21)/(x^3+8x^2-9x-72)
vertical asymptotes
x=3, x=-8
hole
(-3,-2/15)
Simplify into one logarithmic expression
2log5x - 3log5z + (1/2)log5w - (1/2)log5y4
log5[(x2w(1/2))/(z3y2)]
Ari decides to invest $3000 for his future retirement. He invests his money in an account that compounds quarterly at an interest rate of 6%.
Fiona decides to invest for her future retirement as well. She invests $2000 at 7% and it compounded monthly.
In how many years would they have the same amount of money? How much money will they have at that time?
39.6 years
$31697.63
Find the intersection point(s), if any, of the following functions.
f(x)=2/(x^2-1)
g(x)=1/(x+1)
(3, 0.25)
Find all zeros of the polynomial given that -2 is a zero of multiplicity 2.
p(x) = x5 -3 x3 - 16x2 - 108x - 144
-2, -2, 4, 3i, -3i
Describe the end behavior of the function
(2x^2+x-1)/(x^2-9)
The ends of the graph approach a horizontal asymptote of y = 2
Solve
log6(x-3) = log88
9
Kylan borrows $5000 from his family to purchase a used car. He arranges to pay his family the entire loan plus interest in a lump sum in 5 years. If his family is only charging him 2% interest compounded monthly, how much interest will he have to pay?
$525.39
Which of the following points is a solution to this system of inequalities? (Name them all)
y>=(x-2)^2 and y<-x+4
A. (0, 4)
B. (2, 0)
C. (3, 1)
D. (2, 2)
E. (1, 3)
B and D