Question

Write a polynomial that represent the product of 3 consecutive odd integers the first one being 2x-1

Answer 1

Here, if we take a closer look, putting any integral value of x, we will always get an odd number as multiplying by 2 will give an even number and then subtracting 1 will give on odd number.

The first odd number is : 2x - 1.

Consecutive odd numbers differ by 2.
For example, 3, 5, 7.

So, the second consecutive odd number is : 2x + 1 and 2x + 3

. ° . The required polynomial is

(2x - 1) (2x + 1) (2x + 3)
= (4x² - 1) (2x + 3)
= 8x³ + 12x² - 2x - 3

Hope you understand.