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5.2
Dividing Polynomials
DIVIDING BY A MONOMIAL
Example 1:
Example 2
Simplify.
16c d  24c d  8c d e
2 2
2c d
4
5
2
5
4
Remember
6 3791
Example 3
Polynomial Long Division
- Same format as dividing numbers.
Use FILLERS!
 Divide x3 – 4x2 + 8 by x – 1
Example 4: Simplify: (4x2 – 9)(2x + 3)–1
Example 5:
a. (4x4 + 2x3 – 20x – 8) divided by (2x – 3)
Synthetic Division
- Used when divisor is in the form x – k.
- Polynomial must be in standard form. Use FILLERS if terms are
missing!
- Create a polynomial out of coefficients that are left under the line.
- The power of the first term is one less than the degree of the dividend.
- The final number is the remainder.
Example 6:
a. x4 + 3x3 –x2 + 8 by x – 1
Example 7: Use synthetic division.
2x3 + 13x – 7 by x + 6
Example 8:
Use synthetic division.

5.2 Day 1 Ticket out
1. Divide 3x2y5 + 5xyz5 – 6x3y2z4 by 15xy2z3
2. Divide using synthetic division.
2x3 – 7x2 – x – 12 by x – 4
 2m p 
5
3. Simplify
4mp
2 2
4