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SYNTHETIC DIVISION WORKSHEET, Exercises of Calculus

SYNTHETIC DIVISION WORKSHEET. • Don't forget ZERO Coefficients for missing degrees. • Solve the binomial divisor equal to zero. • Multiply and Add Patterns.

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2021/2022

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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?
A.
)6()2925115( 234 ppppp
B.
)2()42108( 234 yyyyy
C.
)4()205328( 45 vvvv
D.
)13()61743( 23 xxxx
E.
)32()12864( 23 vvvv
F.
)12()2356( 23 xzzz
2) Completely FACTOR each polynomial given a known factor.
What are all of the zeros of the polynomial?
A.
5;1523923 xxxx
B.
3;2514
23 xxxx
C.
D.
12;176 23 xxx
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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? A.(^5112529 ) (^6 ) 4 3 2 pppp   p  B.( 8 10 2 4 ) ( 2 ) 4 3 2 yyyy   y  C.(^8 32520 ) (^4 ) 5 4 vvv   v

D.(^3 4176 ) (^31 )

3 2

x  x  x   x 

E.( 4 6 8 12 ) ( 2 3 )

3 2 vvv   v  F.(^6 532 ) (^21 ) 3 2 zzz   x

  1. Completely FACTOR each polynomial given a known factor. What are all of the zeros of the polynomial? A.^9 2315 ;^5 3 2 xxxx  B.^1425 ;^3 3 2 xxxx

C.^25 15013130 ;^53

3 2 xxxx  D.^6 71 ;^21 3 2 xxx

  1. 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.^7 5 3 x ^ xx  B.^2 4 3 2 x ^ xxx  C.^27 3 x  D.^6 3 2 x ^ xx  E.^3 2 x ^ x  F.^4 2 x
  2. 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.^4

3 2

x ^ x  x  B.^14

4 3 2

x  x  x  x 

C.^5

3 2

x ^ x  x  D.^4

3 2

x  x  x 

E.^3

4 3 2

x ^ x  x  x  F.^3

3 2

x  x  x 