Dividing a polynomial by an integer or an expression is really just another way of simplifying.
There isn’t actually anything new to learn: you just need to be able to simplify numbers (like 20/15 simplifies down to 4/3) and know how to divide with indices (when you divide with indices, you subtract the powers. So x^7 / x^3 = x^4).
To divide a polynomial by a number (or integer), there are 3 simple steps to follow:
(1) Rewrite the question as a fraction.
(2) Split the problem into pieces by writing each term over the denominator.
(3) Finish by simplifying each term.
EXAMPLE: (8a + 10b - 14) / 2.
(1) Rewrite as a fraction (8a + 10b - 14) / 2
(2) Split it up 8a/2 + 10b/2 - 14/2.
(3) 8a divided by 2 is 4a. 10b divided by 2 is 5b. And 14 divided by 2 is 7.
ANSWER: 4a + 5b - 7.
Simple!! We follow the same 3 simple steps for dividing by monomials too (remember that a monomial is an expression with just one variable in).
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