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Algebra 2
6.2 Dividing Polynomials
Name: _______________________
Essential Question: How do we divide polynomials using long division & synthetic division?
Warm Up:
Vocabulary:
Synthetic Division – a simpler process of dividing a ____________________ by a ___________________
Examples:
5a 2b − 15ab 3 + 10a 3b 4
1. Simplify
5ab
2. Use long division to find (x 2 − 2x − 15) ÷ (x − 5)
3. Which expression is equal to (a 2 − 5a + 3)(2 − a)−1 ?
A. a + 3
B. −a + 3 +
3
2−a
C. −a − 3 +
3
2−a
D. −a + 3 −
3
2−a
Synthetic Division:
o Write the coefficients of the polynomial so the degrees are descending and write the constant of x
– r in the box and bring down the first coefficient
o Multiply the first coefficient by r and write the product under the second coefficient
o Add the product and the second coefficient
o Repeat steps two and three until you reach a sum in the last column. The numbers along the
bottom row are the coefficients of the quotient, the power is one less than the degree of the
dividend. The final number is the remainder.
4. Use synthetic division to find the following.
a. (x 3 − 4x 2 + 6x − 4) ÷ (x − 2)
b. (4y 3 − 6y 2 + 4y − 1) ÷ (2y − 1)
Summarizer: Would you rather use long division or synthetic division to divide polynomials? Explain why.
(You may be asked to write this answer with your name on it)