Synthetic division clearly simplifies the long division process for dividing by a ...
there is a way to use synthetic division when dividing by a linear expression of ...
5-A Worksheet
Per:
Name:
Extensions of Synthetic Division
Honors Algebra 3-4
Synthetic division clearly simplifies the long division process for dividing by a linear expression x − a, but there is a way to use synthetic division when dividing by a linear expression of the form ax − b where a > 1. 1. Consider dividing 6x3 − 11x2 − 5x + 12 by 2x − 3. a. Use long division to divide 6x3 − 11x2 − 5x + 12 by 2x − 3.
b. Use synthetic division to divide 6x3 − 11x2 − 5x + 12 by x − 3 . 2
c. How does the divisor in Exercise 2, x − 3 , compare to the divisor, 2x − 3, in Exercise 1? 2
d. How does the quotient in Exercise 2 compare to the quotient in Exercise 1?
e. In order to use synthetic division to divide 6x3 − 11x2 − 5x + 12 by 2x − 3, you can divide by x − 3 . 2 How will you adjust your quotient in order to have the correct answer?
2. Repeat this process to divide 3 x 3 − 8 x 2 + 7 x − 4 by 3 x − 2
3. What do you notice about the remainders? This is important.
4. Use this new method to perform the following divisions: a.
(4 x
3
+ 7 x 2 − 62 x + 15 ÷ (4 x − 1)
)
b.
(2 x
3
+ 17 x 2 + 47 x + 45 ÷ (2 x + 7 ) (notice the sign)
)
5. Given that − 3 + 11 is one of the zeros of f ( x ) = x 4 + 6 x 3 − 7 x 2 − 30 x + 10 , and what you know about conjugates and roots, find all the zeros of f ( x ) .
6. Given that 2 − i is one of the zeros of g ( x ) = x 5 − 6 x 4 + 11x 3 − x 2 − 14 x + 5 , and what you know about complex conjugates and roots, find all the zeros of g ( x ) .
7. EXTRA CREDIT: (rare, but worth it) Research to find out how to synthetically divide a. x 4 + 6 x 3 − 11x 2 − 5 x + 12 by the quadratic expression x 2 + 2 x − 3 . b. x 4 + 6 x 3 − 1x 2 − 5 x + 12 by the cubic expression x 3 + 2 x 2 − 9 x + 25 .
