The product of two consecutive odd integers is 1 less than twice their sum. Find the integers.

Two consecutive odd integers are and , for some integer .

Their product is .

Twice their sum is

Since the product is 1 less than twice the sum, we have

So, we have

If , the integers are 3 and 5

If , the integers are -1 and 1.

In both cases, in fact, we have:

(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

51840000 cm 2

step-by-step explanation: