How do you divide polynomials by whole numbers?

To divide a polynomial by a whole number, you essentially divide each term of the polynomial by that whole number. This is done by splitting the problem into individual terms and simplifying each one.

Here's a breakdown of the process:

1. Split the polynomial: Divide each term of the polynomial by the whole number (denominator).
2. Simplify: Simplify each term individually.

Example

Let's say we want to divide the polynomial 8a + 10b by the whole number 2.

1. Split the polynomial: We rewrite the expression as (8a / 2) + (10b / 2).
2. Simplify:
   • 8a / 2 = 4a
   • 10b / 2 = 5b

Therefore, (8a + 10b) / 2 = 4a + 5b.

Another example

• Divide the polynomial 12x^2 + 6x - 9 by the whole number 3.
  1. Split the polynomial: (12x^2 / 3) + (6x / 3) - (9 / 3).
  2. Simplify
     • 12x^2 / 3 = 4x^2
     • 6x / 3 = 2x
     • 9 / 3 = 3

Therefore, (12x^2 + 6x - 9) / 3 = 4x^2 + 2x - 3.