Unit Test — Unit test Answers

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What is the factored form of the binomial expansion 256x2 + 288xy + 81y2?

A
(4x – 3y)4
B
(4x + 3y)4
C
(16x – 9y)2
D
(16x + 9y)2
2
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What are the coefficients for the binomial expansion of (a + b)3?

A
1, 4, 6, 4, 1
B
1, 1
C
1, 2, 1
D
1, 3, 3, 1
3

Which of the following is the complete list of roots for the polynomial function ?

Question illustration
A
–5, 3
B
–5, 3, –4 + i, –4 – i
C
–5, 3, –4 + i, 4 + i
D
–4 + i, –4 – i
4

What is the ninth term in the binomial expansion of (x – 2y)13?

A
329,472x5y8
B
–329,472x5y8
C
–41,184x8y5
D
41,184x8y5
5

The area of a rectangle is (x3 – 5x2 + 3x – 15), and the width of the rectangle is (x2 + 3). If area = length × width, what is the length of the rectangle?

A
x + 5
B
x – 15
C
x + 15
D
x – 5
6

If 5 + 6i is a root of the polynomial function f(x), which of the following must also be a root of f(x)?

A
–5 – 6i
B
5 – 6i
C
6 – 5i
D
6 + 5i
7

Anja divides (8x3 – 36x2 + 54x – 27) by (2x – 3) as shown below. What error does Anja make?

Question illustration
A
She makes a subtraction error.
B
She makes an error choosing the x-term in the quotient.
C
She makes a multiplication error.
D
She makes an error rewriting the problem in long division.
8

What is the quotient of (2x4 – 3x3 – 3x2 + 7x – 3) ÷ (x2 – 2x + 1)?

A
2 x Superscript 4 Baseline minus 3 x cubed minus eleven-halves
Option A
B
2x2 + x – 3 –
Option B
C
2x2 – x
D
2x2 + x – 3
9

Which statement describes the graph of this polynomial function?

Question illustration
A
The graph crosses the x-axis at x = 2 and x = –1 and touches the x-axis at x = 0.
B
The graph touches the x-axis at x = 2 and x = –1 and crosses the x-axis at x = 0.
C
The graph crosses the x-axis at x = –2 and x = 1 and touches the x-axis at x = 0.
D
The graph touches the x-axis at x = –2 and x = 1 and crosses the x-axis at x = 0.
10

What is the remainder when (3x3 – 2x2 + 4x – 3) is divided by (x2 + 3x + 3)?

A
30
B
3x – 11
C
28x – 36
D
28x + 30
11

The side length, s, of a cube is 3x + 2y. If V = s3, what is the volume of the cube?

A
3x3 + 18x2y + 36xy2 + 8y3
B
27x3 + 54x2y + 18xy2 + 2y3
C
27x3 + 18x2y + 12xy2 + 2y3
D
27x3 + 54x2y + 36xy2 + 8y3
12

Which statement about the simplified binomial expansion of (a + b2)n, where n is a positive integer, is true?

A
The exponent of b will always be even.
B
The exponent of a will always be odd.
C
The sum of the exponents of a and b will always equal n.
D
The sum of the exponents of a and b will always equal n – 1.
13

One root of a third degree polynomial function f(x) is –5 + 2i. Which statement describes the number and nature of all roots for this function?

A
f(x) has two real roots and one imaginary root.
B
f(x) has two imaginary roots and one real root.
C
f(x) has three imaginary roots.
D
f(x) has three real roots.
14

Which polynomial can be factored using the binomial theorem?

A
81x2 + 117x + 169
B
81x2 + 234x + 169
C
6,561x4 – 9,477x3 + 13,689x2 – 19,773x + 28,561
D
6,561x4 – 18,954x3 + 27,378x2 – 39,546x + 28,561
15

The polynomial is missing the coefficient of the second and third terms.1,000x3 + ___x2y + ___xy2 + 1,331y3If the polynomial is factorable using the binomial theorem, what is the coefficient of x2y?

A
3,300
B
3,630
C
4,400
D
4,840

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