Question

Divide 20a5b3 by 5a2b.

4a3b2
4a3b3
4a3b4
4a7b4
Question 2(Multiple Choice Worth 4 points)
(06.04 MC)

Choose the correct simplification of (6x − 5)(2x2 − 3x − 6).

12x3 + 28x2 + 21x + 30
12x3 − 28x2 − 21x + 30
12x3 + 28x2 − 21x + 30
12x3 − 28x2 − 21x − 30
Question 3(Multiple Choice Worth 4 points)
(06.04 MC)

The expression 60x + 4 represents the amount of money Mike earns making custom tables. The expression 2x − 4 represents his upfront costs. If x represents the number of tables sold in both expressions, what is Mike's profit when he sells 4 tables?

$8
$240
$61
$244
Question 4(Multiple Choice Worth 4 points)
(06.02 LC)

Choose the correct simplification of (7x3 − 8x − 5) + (3x3 + 7x + 1).

10x3 − x − 4
10x3 + x + 4
4x3 − 15x − 6
4x3 + 15x + 6
Question 5(Multiple Choice Worth 4 points)
(06.04 MC)

Which expression is equivalent to the area of metal sheet required to make this square-shaped traffic sign?

A square shaped traffic sign is shown with the length of one side labeled as x plus 1.

x2 + 2x + 1
x2 + x + 1
x2 + 2x
x2 + 1
Question 6(Multiple Choice Worth 4 points)
(06.02 MC)

The expression 3x − 10 represents the time it takes a commuter to travel in the morning to work. The expression 12x + 8 represents the time it takes a commuter to travel in the evening from work. What is the total travel time?

15x − 2
9x − 2
15x + 2
9x + 2
Question 7(Multiple Choice Worth 4 points)
(06.04 MC)

The function f(x) = x + 3 represents the length of a rectangle. The function g(x) = 12x − 5 represents the width of the rectangle. Use (f ⋅ g)(3) to determine the area of the rectangle.

186
37
31
6
Question 8(Multiple Choice Worth 4 points)
(06.02 MC)

Simplify (4x3y − 5x2y + 6y) − (9x3y − 3x2y − 6y).

−5x3y − 7x2y + 12y
−5x3y − 2x2y + 12y
−5x3y + 8x2y
−5x3y − 2x2y
Question 9(Multiple Choice Worth 4 points)
(06.02 MC)

Choose the correct simplification and demonstration of the closure property given: (2x3 + x2 − 4x) − (9x3 − 3x2).

−7x3 + 4x2 − 4x; may or may not be a polynomial
−7x3 + 4x2 − 4x; is a polynomial
11x3 − 2x2 − 4x; may or may not be a polynomial
11x3 − 2x2 − 4x; is a polynomial
Question 10(Multiple Choice Worth 4 points)
(06.03 LC)

Choose the correct simplification of a to the 5th power times b to the 6th power all over a to the 4th power times b to the 4th power.

a9b10
ab2
1 over a times b to the 2nd power
1 over a to the 9th power times b to the 10th power
Question 11(Multiple Choice Worth 4 points)
(06.03 LC)

Simplify (4x3y3)(2x2y).

6x5y4
8x5y3
8x6y3
8x5y4
Question 12(Multiple Choice Worth 4 points)
(06.02 MC)

Simplify (3x3y2 − 5xy4 − 2xy) + (2x3y2 + 5xy4 + 3xy).

5x3y2 − 2xy4 + xy
5x3y2 − 2xy4 − 5xy
5x3y2 + xy
5x3y2 − xy
Question 13(Multiple Choice Worth 4 points)
(06.04 MC)

Divide 15x4 − 5x3 − 10x2 by −5x2.

−3x2 + x − 2
−3x2 + x + 2
−3x2 − 10x + 2
10x2 − 10x − 15
Question 14(Multiple Choice Worth 4 points)
(06.03 MC)

Choose the correct simplification of (2xy2)2(y2)3.

2x2y10
4x2y9
4x2y10
2x2y9
Question 15(Multiple Choice Worth 4 points)
(06.04 LC)

Choose the correct simplification of 7x2(6x + 3x2 − 4).

21x4 − 42x3 + 28x2
42x4 + 21x3 − 3x2
21x4 + 42x3 − 28x2
42x4 − 13x3 + 11x2

Answer 1

Here are the answers to the multiple-choice questions provided:

### Question 1:
**Divide 20a5b3 by 5a2b.**
To divide the expression, we simplify it:
\[
\frac{20a^5b^3}{5a^2b} = \frac{20}{5} \cdot \frac{a^5}{a^2} \cdot \frac{b^3}{b} = 4a^{5-2}b^{3-1} = 4a^3b^2
\]
**Answer:** 4a3b2

---

### Question 2:
**Choose the correct simplification of (6x − 5)(2x^2 − 3x − 6).**
Using the distributive property:
1. \(6x \cdot 2x^2 = 12x^3\)
2. \(6x \cdot (-3x) = -18x^2\)
3. \(6x \cdot (-6) = -36x\)
4. \(-5 \cdot 2x^2 = -10x^2\)
5. \(-5 \cdot (-3x) = 15x\)
6. \(-5 \cdot -6 = 30\)

Adding them up:
\[
12x^3 + (-18x^2 - 10x^2) + (-36x + 15x) + 30 = 12x^3 - 28x^2 - 21x + 30
\]
**Answer:** 12x3 − 28x2 − 21x + 30

---

### Question 3:
**What is Mike's profit when he sells 4 tables?**
Profit = Earnings - Costs
Earnings: \(60x + 4\)
Costs: \(2x - 4\)

Calculating profit:
Profit when \(x = 4\):
Earnings:
\[
60(4) + 4 = 240 + 4 = 244
\]
Costs:
\[
2(4) - 4 = 8 - 4 = 4
\]
Profit:
\[
244 - 4 = 240
\]
**Answer:** $240

---

### Question 4:
**Choose the correct simplification of (7x^3 − 8x − 5) + (3x^3 + 7x + 1).**
Combining like terms:
1. \(7x^3 + 3x^3 = 10x^3\)
2. \(-8x + 7x = -x\)
3. \(-5 + 1 = -4\)

Overall:
\[
10x^3 - x - 4
\]
**Answer:** 10x3 − x − 4

---

### Question 5:
**Which expression is equivalent to the area of a square with side \(x+1\)?**
The area of a square = side^2:
\[
(x + 1)^2 = x^2 + 2x + 1
\]
**Answer:** x² + 2x + 1

---

### Question 6:
**What is the total travel time?**
Total time = Morning + Evening:
\[
(3x - 10) + (12x + 8) = 3x - 10 + 12x + 8 = 15x - 2
\]
**Answer:** 15x − 2

---

### Question 7:
**Use (f ⋅ g)(3) to determine the area of the rectangle.**
1. \(f(3) = 3 + 3 = 6\)
2. \(g(3) = 12(3) - 5 = 36 - 5 = 31\)
Area = Length × Width = \(6 \cdot 31 = 186\)
**Answer:** 186

---

### Question 8:
**Simplify (4x³y − 5x²y + 6y) − (9x³y − 3x²y − 6y).**
Combining like terms:
1. \(4x^3y - 9x^3y = -5x^3y\)
2. \(-5x^2y + 3x^2y = -2x^2y\)
3. \(6y + 6y = 12y\)

Overall:
\[
-5x^3y - 2x^2y + 12y
\]
**Answer:** -5x³y − 2x²y + 12y

---

### Question 9:
**Choose the correct simplification and demonstration of the closure property given:**
Combining the expressions:
\[
(2x^3 + x^2 - 4x) - (9x^3 - 3x^2) = -7x^3 + 4x^2 - 4x
\]
Since it is a polynomial, the answer is:
**Answer:** −7x³ + 4x² − 4x; is a polynomial

---

### Question 10:
**Choose the correct simplification of $\frac{a^5b^6}{a^4b^4}$.**
Using the rules of exponents:
\[
a^{5-4}b^{6-4} = ab^2
\]
**Answer:** ab²

---

### Question 11:
**Simplify (4x³y³)(2x²y).**
Using the multiplication of powers:
\[
(4 \cdot 2)(x^{3+2})(y^{3+1}) = 8x^5y^4
\]
**Answer:** 8x^5y^4

---

### Question 12:
**Simplify (3x³y² − 5xy⁴ − 2xy) + (2x³y² + 5xy⁴ + 3xy).**
Combining like terms:
1. \(3x^3y^2 + 2x^3y^2 = 5x^3y^2\)
2. \(-5xy^4 + 5xy^4 = 0\)
3. \(-2xy + 3xy = xy\)

Overall:
\[
5x^3y^2 + xy
\]
**Answer:** 5x³y² + xy

---

### Question 13:
**Divide 15x⁴ - 5x³ - 10x² by -5x².**
Performing the division:
\[
\frac{15x^4}{-5x^2} = -3x^{4-2} = -3x^2
\]
\[
\frac{-5x^3}{-5x^2} = x^{3 - 2} = x
\]
\[
\frac{-10x^2}{-5x^2} = 2
\]
Combining terms:
\[
-3x^2 + x + 2
\]
**Answer:** -3x² + x + 2

---

### Question 14:
**Choose the correct simplification of (2xy²)²(y²)³.**
Using the power rule:
\[
(2^2)(x^2)(y^{2*2})y^{6} = 4x^2y^{4 + 6} = 4x^2y^{10}
\]
**Answer:** 4x²y^{10}

---

### Question 15:
**Choose the correct simplification of 7x²(6x + 3x² − 4).**
Distributing 7x²:
\[
7x^2(6x) + 7x^2(3x^2) - 7x^2(4) = 42x^3 + 21x^4 - 28x^2
\]
Arranging:
\[
21x^4 + 42x^3 - 28x^2
\]
**Answer:** 21x⁴ + 42x³ − 28x²

---

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