Polynomials
Factor the following expression completely
2x^3+3x^2-32x-48
What is
(x-4)(x+4)(2x+3)
Simplify the following radical completely
root(3)(750x^6y^2)
What is
(5x^2)root(3)(6y^2)
Rewrite the following in logarithmic form 4x=256
What is log4256 = x?
Simplify the following:
(x^2+4x-21)/(x^2-49)
What is
(x-3)/(x-7)
Find the probability that you roll a 2 on a standard 6-sided die, then pull a red card out of a deck of cards.
P(2 and red) = 1/12
Factor the following expression completely
x^3-64
What is
(x-4)(x^2+4x+16)
Simplify the following radical completely
sqrt(10)(5sqrt(5) - 2sqrt(2))
What is
25sqrt(2) - 4sqrt(5)
Condense the following logarithmic expression completely
log3x - 5log3y
What is
log3(x/y5)
Simplify the following:
(15xy^3)/(2y^2) * (4x^3y)/(45x^3y)
What is
(2y)/(3)
You are pulling markers out of a bag without replacing them. There are 3 red, 5 green, 2 yellow, and 8 blue markers. Find the probability of pulling a red marker, then a yellow marker.
P(red, yellow) = 1/51
Factor the following expression completely
8x^4+10x^2-3
What is
(2x^2+3)(2x+1)(2x-1)
Simplify the following radical completely
root(4)(25x^2)
What is
sqrt(5x)
Expand the following log completely
log_5(x*sqrt(y)*z^3)
What is
log_5x + (1/2)log_5y + 3log_5z
Simplify the following:
x/(x-4) - x/(x+3)
What is
(7x)/((x-4)(x+3))
Pablo plans to rearrange the letters in the word Flamingo. Identify if this is a permutation or a combination, then find the total number of possible outcomes.
What is a permutation, with 40320 options?
Solve the following equation
5x^4-80x
What is
x=0, x = +-2i, x = +-2
Simplify the following radical completely
4sqrt(98) + sqrt(150) - 2sqrt(32)
What is
20sqrt(2) + 5sqrt(6)
Solve the following logarithmic equation
log_3(2p-5)=2log_3(6)-log_3(4)
What is p=7?
Simplify the following:
(5x^2+20x)/(16-x^2) / (15x^2)/(x^2-11x+28)
What is
(-(x-7)/(3x))
The dance company is choosing 3 new dancers from a group of 25 who try out. Identify if this is a combination or a permutation, and find how many ways they can choose the new dancers.
What is a combination with 2300 combinations?
Solve the following equation
x^3-216
What is
x=6, x=-3 +- 3isqrt(3)
Solve the following equation, check for extraneous solutions
sqrt(2x+3) = x + 2
What is
x = -1
Solve the following logarithmic equation, check for extraneous solutions
log(x-3) + log(x) = 1
What is x = 5?
Solve the following:
(x + 10/(x-9) = 2)
What is x = 4, x = 7?
Jane takes a multiple-choice test with 25 questions, each with 4 options. She guesses on each question. Find the probability that she gets exactly 8 questions correct.
What is 0.124 or 12.4%?