Division of Polynomials

1. DIVISION OF
POLYNOMIALS
FEBRUARY 13, 2023

2. Recall
Laws of Exponents in Division
𝑥6
𝑥2 = 𝑥6−2
= 𝑥4

3. Recall
Laws of Exponents in Division
𝑎7𝑏8
𝑎2𝑏4=𝑎7−2𝑏8−4
=𝑎5
𝑏4

4. Remember:
-to divide exponential variables, copy
the variable/s and subtract their
exponents.

5. Division of Polynomials
To divide polynomial by a
monomial, divide each term of the
polynomial by the monomial.

6. Example 1
4𝑥3+ 12𝑥3+8𝑥
4𝑥
=
4𝑥3
4𝑥
+
12𝑥2
4𝑥
+
8𝑥
4𝑥
= 𝑥2 + 3𝑥 + 2

7. Example 2
33𝑥 −55
11
=
33𝑥
11
−
55
11
=3x - 5

8. Example 3
144𝑎2− 72𝑎3+ 60𝑎2𝑏3
12𝑎2
=
144𝑎2
12𝑎2 −
72𝑎3
12𝑎2 +
60𝑎2𝑏3
12𝑎2
= 12 − 6𝑎 + 5𝑎𝑏

9. Example 4
5𝑥3− 15𝑥4𝑦+ 35𝑥2𝑦3
−5𝑥2
=
5𝑥3
−5𝑥2 −
15𝑥4𝑦
−5𝑥2 +
35𝑥2𝑦3
−5𝑥2
= x + 3𝑥2𝑦 − 7𝑦3

10. Example 5
12𝑎5𝑏− 15𝑎4𝑏4+ 21𝑎3𝑏
3𝑎3𝑏3
=
12𝑎5𝑏
3𝑎3𝑏3 −
15𝑎4𝑏4
3𝑎3𝑏3 +
21𝑎3𝑏
3𝑎3𝑏3
= 4𝑎2
𝑏−2
− 5𝑎𝑏 + 7𝑏−2
(avoid negative exponents)
=
4𝑎2
𝑏2 − 5𝑎𝑏 +
7
𝑏2 ( if the exp. Is negative, bring it to the denominator)

11. Try these
1.
24𝑥−12𝑦
12
4.
25𝑎3−35𝑎2
5𝑎2
2.
3𝑥4𝑦3 −6𝑥3𝑦4+9𝑥3𝑦5
3𝑥3𝑦3
3.
4𝑥−8
4