Hon Math III: Unit 4




SYNTHETIC DIVISION WORKSHEET
Don’t forget ZERO Coefficients for missing degrees
Solve the binomial divisor equal to zero.
Multiply and Add Patterns
If zero value is a fraction, then divide all coefficients by denominator.
1) Perform the following divisions using Synthetic Division.
Is the binomial divisor a factor of the polynomial?
3
2
A. ( p4  5 p 3  11 p 2  25 p  29)  ( p  6)
D. ( 3 x  4 x  17 x  6)  ( 3 x  1)
4
3
2
B. ( y  8 y  10 y  2 y  4)  ( y  2)
E. (4v 3  6v 2  8v  12)  (2v  3)
C. (8v 5  32v 4  5v  20)  (v  4)
3
2
F. (6z  5z  3z  2)  (2 x  1)
2) Completely FACTOR each polynomial given a known factor.
What are all of the zeros of the polynomial?
3
2
3
2
A. x  9 x  23 x  15; x  5
C. 25 x  150 x  131 x  30; 5 x  3
3
2
B. x  x  14 x  24; x  3
3
2
D. 6 x  7 x  1; 2 x  1
3) For each polynomial, LIST all POSSIBLE RATIONAL ROOTS.
 Find all factors of the leading coefficient and constant value of polynomial.
 ANY RATIONAL ROOTS = ± (Constant Factor over Leading Coefficient Factor)
A. x 5  7 x 3  3 x  12
B. x 4  2 x 3  8 x 2  16 x  32 C. x 3  27
D. 6 x 3  7 x 2  3 x  1
E. 3 x 2  2 x  2
F. 4 x 2  9
4) Completely FACTOR and find all zeros for each polynomial:
 List all POSSIBLE RATIONAL ZEROS (Section #3)
 Use Synthetic Division to check each zero. (Section #2)
 When you reach a quadratic equation, perform regular factoring or Quadratic Formula.
A. x  4 x  5 x  2
B. x  x  14 x  16 x  32
C. 5 x  29 x  19 x  5
D. 4 x  9 x  6 x  1
E. 3 x  10 x  24 x  6 x  5
F. 3 x  9 x  4 x  12
3
2
3
4
2
3
2
4
3
3
3
2
2
2