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Arithmetic
Geometric
Division of Polynomials
Remainder & Factor Theorem
100

Which of the following is an arithmetic sequence?

A. 3, 6, 12, 24, 48

B. 5, 10, 15, 20, 25

C. 2, 4, 8, 16, 32

D. 100, 50, 25, 12.5

B. 5, 10, 15, 20, 25

100

In the geometric sequence 2,6,18,54,…, what is the common ratio?

A. 2
B. 3
C. 4
D. 6  

B. 3

100

In the polynomial 2x + 7x4 − 5x3 − 9, what is the leading term?

A. 7x4
B. −5x3
C. 2x
D. −9 

A. 7x4

100

Find the remainder when x3−4x2+x+6 is divided by x−2.

A. 0
B. 2
C. −2
D. 4 

A. 0

200

Which Statement is TRUE? 

A. In an arithmetic sequence, the difference between consecutive terms is constant.
B. In an arithmetic sequence, the ratio between terms is always the same.
C. The common difference of an arithmetic sequence can only be positive.
D. In an arithmetic sequence, the terms always increase.

A.

200

Which is NOT a Geometric Sequence?

A. 3, 6, 12, 24, 48
B. 81, 27, 9, 3, 1
C. 5, 10, 15, 20, 25
D. 1, 1/2, 1/4, 1/8, 1/16  

C. 5, 10, 15, 20, 25

200

What is the degree of the polynomial
6x5−4x3+8x−1?

A. 3
B. 4
C. 5
D. 6  

C. 5

200

If the remainder is zero, then the quotient is ___.

A. not a factor
B. a constant
C. a factor
D. not a constant

C. a factor

300

Which is NOT an Arithmetic Sequence?

A. 4, 7, 10, 13, 16
B. 5, 6, 7, 8, 9
C. 10, 8, 6, 4, 2
D. 2, 4, 8, 16, 32

D. 2, 4, 8, 16, 32

300

Which Statement is TRUE?

A. In a geometric sequence, the difference between consecutive terms is constant.
B. In a geometric sequence, the ratio between consecutive terms is constant.
C. In a geometric sequence, the common ratio must be greater than 1.
D. All geometric sequences increase.  

B.

300

Find the quotient when (x2+5x+6) is divided by (x+2).

A. x+3
B. x+2
C. x+4
D. x+5 

A. x+3

300

Which Statement is TRUE? 

A. The Remainder Theorem says the remainder is always zero.
B. The Factor Theorem says x−r is a factor of P(x) if and only if f(r)=0.
C. The Remainder Theorem is only used for degree 2 polynomials.
D. The Factor Theorem can only be used when the common ratio is constant.

B

400

Insert two arithmetic means between 6 and 18. That is: 6, ___, ____, 18. What are they?

A. 8, 10
B. 8, 14
C. 10, 14
D. 9, 12  

C. 10, 14

400

Insert two geometric means between 4 and 108. That is: 4, ___, ___, 108.  What are they? 

A. 12, 36
B. 9, 27
C. 18, 54
D. 8, 16


A. 12, 36

400

Find the quotient when 2x2−3x−9 is divided by x−3.

A. 2x+3
B. 2x−3
C. 2x+1
D. 2x−1

A. 2x+3

400

Which of the following is a factor of x3−6x2+11x−6?

A. x−1
B. x+2
C. x−4
D. x+3

A. x−1

500

Find the sum of the first 10 terms of the arithmetic sequence: 5, 8, 11, 14, … 

A. 170
B. 175
C. 180
D. 185

D. 185

500

Find the sum of the infinite geometric series: 

12,  4,  4/3,  4/9,  ...

A. 18
B. 17
C. 16
D. 15

A.  18

500

Find the quotient when 4x3 + 8x2 − 5x − 10 is divided by x+2.

A. 4x2 + 5x − 5
B. 4x2 − 5x + 5
C. 4x2 + 5
D. 4x2 − 5

D. 4x2 − 5

500

If x−3 is a factor of 2x3−9x2+kx−27, what is the value of k?

A. 15
B. 18
C. 20
D. 24  

B. 18