Algebra Answers

Explain the difference between round and hard brackets when expressing intervals. Use an example to justify

When a polynomial is divided by x + 1, the remainder is 5. When the same polynomial is divided by x – 1, the remainder is 1. When the same polynomial is divided by x – 2, the remainder is 20. Determine the remainder when the polynomial is divided (x + 1)(x – 1)(x – 2).

Consider the polynomial function 𝑃(𝑥) = 2𝑥^3 − 𝑚𝑥^2 + 𝑥 − 5𝑚. The remainder when P(x) is divided by (𝑥 − 2) is four times the remainder from dividing P(x) by (𝑥 + 1). Determine m algebraically and show all your work. 

Consider the polynomial function 𝑃(𝑥) = 2𝑥^3 − 𝑚𝑥^2 + 𝑥 − 5𝑚. The remainder when P(x) is divided by (𝑥 − 2) is four times the remainder from dividing P(x) by (𝑥 + 1). Determine m algebraically and show all your work. 

Find the producer's surplus at Q = 9 for the following supply functions:

(a) P = 12 + 2Q

(b) P = 20√Q + 15

8. If the investment flow is

f(t) = 5000t ^ (1/4)

calculate the capital formation from the end of the second year to halfway through the fifth year. Give your answer to the nearest whole number.

Given that 2𝑥 − 5 is a factor of polynomial functions 𝑓(𝑥) = 𝑘𝑥^2 − 𝑏𝑥 + 3𝑘, determine the ratio k : b in the simplest form.

Unity Games is a company that sells video games. Its revenue last year was modelled by

the function 𝑔(𝑥) = − 4𝑥^4 + 6𝑥(4𝑥 − 1) − 4 and its revenue this year is modelled by the function 𝑓(𝑥) = − 3𝑥^2(𝑥^2 − 8) − 6𝑥 − 5 where x is the number of video games sold in thousands and revenue is in millions of dollars. Determine the range of values for the number of video games sold that makes the revenue this year greater than the revenue last year. You must use a full algebraic solution.

Solve the following equations.

a) x^3 + x = 4x^2 - 6

b) 3x^4 - 5x^2 + 2 = 0

. Soldiers are marching in a parade. There are 10 soldiers in a row. What is the rule which gives the number of soldiers, given the number of rows?