AnswersSLPS-1200710-Mathematics for College Algebra - S2 - GFSynthetic Division and the Remainder Theorem

Synthetic Division and the Remainder Theorem — Unit test Answers

15 verified answers
1
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If f(–5) = 0, what are all the factors of the function ? Use the Remainder Theorem.

Question illustration
A
(x – 2)(x + 5)(x – 3)
B
(x + 2)(x – 5)(x + 3)
C
(x – 2)(x + 5)
D
(x + 2)(x – 5)
2
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What are the solutions of the equation (x + 2)2 + 12(x + 2) – 14 = 0? Use u substitution and the quadratic formula to solve.

A
x = negative 8 plus-or-minus 5 StartRoot 2 EndRoot
Option A
B
x = negative 6 plus-or-minus 5 StartRoot 2 EndRoot
Option B
C
x = negative 4 plus-or-minus 5 StartRoot 2 EndRoot
Option C
D
x = negative 2 plus-or-minus 5 StartRoot 2 EndRoot
Option D
3

Which expression is a possible leading term for the polynomial function graphed below?

Question illustration
A
–18x14
B
–10x7
C
17x12
D
22x9
4

The president of a company creates a graph of the price of the company’s stock over one year. He describes the graph as follows:• The price of the stock rose to about $17 before falling to about $3.• There have only been two periods during which the price of the stock decreased.• The price of the stock is expected to increase in the long run.Which graph correctly shows the price of the stock?

A
mc026-1.jpg
Option A
B
mc026-2.jpg
Option B
C
mc026-3.jpg
Option C
D
mc026-4.jpg
Option D
5

Which term, when added to the given polynomial, will change the end behavior of the graph? y = 14x8 – 6x5 – 2x4 – 10

A
–6x9
B
–5x7
C
5x8
D
6x10
6

Which polynomial function could be represented by the graph below?

Question illustration
A
f(x) = x2 + x – 2
B
f(x) = 2x2 + 2x – 4
C
f(x) = x2 – x – 2
D
f(x) = 2x2 –2x – 4
7

If (x + k) is a factor of f(x), which of the following must be true?

A
f(k) = 0
B
f(–k) = 0
C
A root of f(x) is x = k.
D
A y intercept of f(x) is x = –k.
8

A function is a sixth-degree polynomial function. How many turning points can the graph of the function have?

A
exactly 5
B
5 or less
C
exactly 6
D
6 or less
9

What are the solutions of the equation x4 – 5x2 – 36 = 0? Use factoring to solve.

A
x = ±2 and x = ±3
B
x = ±2i and x = ±3
C
x = ±2 and x = ±3i
D
x = ±2i and x = ±3i
10

Which expression is a difference of cubes?

A
mc014-1.jpg
Option A
B
mc014-2.jpg
Option B
C
mc014-3.jpg
Option C
D
mc014-4.jpg
Option D
11

What is the end behavior of the graph of the polynomial function f(x) = –x5 + 9x4 – 18x3?

A
As , and as , .
Option A
B
As , and as , .
Option B
C
As , and as , .
Option C
D
As , and as , .
Option D
12

What is the cube root of

Question illustration
A
mc009-2.jpg
Option A
B
mc009-3.jpg
Option B
C
mc009-4.jpg
Option C
D
mc009-5.jpg
Option D
13

A small cube with side length 6y is placed inside a larger cube with side length . What is the difference in the volume of the cubes?

Question illustration
A
mc026-2.jpg
Option A
B
mc026-3.jpg
Option B
C
mc026-4.jpg
Option C
D
mc026-5.jpg
Option D
14

Which statement best describes the equation x5 + x3 – 14 = 0?

A
The equation is quadratic in form because it is a fifth-degree polynomial.
B
The equation is quadratic in form because the difference of the exponent of the lead term and the exponent of the middle term is 2.
C
The equation is not quadratic in form because it cannot be rewritten as a second-degree polynomial.
D
The equation is not quadratic in form because the exponent of the lead term is not the square of the exponent of the middle term.
15

What is the factored form of ?

Question illustration
A
mc022-2.jpg
Option A
B
mc022-3.jpg
Option B
C
mc022-4.jpg
Option C
D
mc022-5.jpg
Option D

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