If Dain wants $50,000 after 3 years to make a down payment on a house, how much does he need to invest every quarter, into an account that pays 6% compounded quarterly?

P = $41,820.01

Step-by-step explanation:

A = P(1 + r/n)^nt

P = A / (1 + r/n)^nt

Where,

P = principal

A = future value = $50,000

n = number of periods = 4

r = interest rate = 6% = 0.06

t = time = 3 years

P = A / (1 + r/n)^nt

= 50,000 / (1 + 0.06/4)^4*3

= 50,000 / (1 + 0.015)^12

= 50,000 / (1.015)^12

= 50,000 / 1.1956

= 41,820.01

P = $41,820.01

(x3 + 6x2 + 2x - 6) • (x - 1)

step-by-step explanation:

polynomial long division :

3.2     polynomial long division

dividing :   x4+5x3-4x2-8x+6

                              ("dividend")

by         :     x-1     ("divisor")

dividend     x4   +   5x3   -   4x2   -   8x   +   6

- divisor   * x3     x4   -   x3            

remainder         6x3   -   4x2   -   8x   +   6

- divisor   * 6x2         6x3   -   6x2        

remainder             2x2   -   8x   +   6

- divisor   * 2x1             2x2   -   2x    

remainder               -   6x   +   6

- divisor   * -6x0               -   6x   +   6

remainder                     0

quotient :   x3+6x2+2x-6   remainder:   0