Question
Multiply (4x + 7)2.
16x2 + 49
16x2 + 28x + 49
16x2 + 56x + 49
8x2 + 14
Question 2(Multiple Choice Worth 1 points)
(01.08 MC)
Multiply (2x2 + 3x − 6)(x − 1).
2x3 + 3x2 − 6x + 6
2x3 − 18x2 − 3x + 6
2x3 − 12x2 + 3x + 6
2x3 + x2 − 9x + 6
Question 3(Multiple Choice Worth 1 points)
(01.08 MC)
Let f(x) = 3x2 + x − 3 and g(x) = x2 − 5x + 1. Find f(x) − g(x).
2x2 − 4x − 2
2x2 − 4x − 4
2x2 + 6x − 2
2x2 + 6x − 4
Question 4(Multiple Choice Worth 1 points)
(01.08 MC)
Let f(x) = x2 + 3x − 4 and g(x) = x + 5. Find f(x) ⋅ g(x).
x3 + 3x2 + 16x − 20
x3 + 5x2 + 14x − 20
x3 + 8x2 + 11x − 20
x3 + 9x2 + 19x − 20
Question 5(Multiple Choice Worth 1 points)
(01.08 MC)
A company makes video games. The price of a video game is modeled by the function p(x) = 30x + 2, where x is the number of years since the company started producing games. The number of video games they sell is modeled by the function s(x) = 500x + 250. To find the total revenue from their video games, the company should use what operation on the polynomials?
Addition
Subtraction
Multiplication
It cannot be determined
Question 6(Multiple Choice Worth 1 points)
(01.08 MC)
Add (3x4 − 2x3 + 1) + (12x4 + x2 − 11).
15x4 − x3 − 10
15x4 − x2 − 10
15x4 − 2x3 + x2 + 10
15x4 − 2x3 + x2 − 10
Question 7(Multiple Choice Worth 1 points)
(01.08 MC)
Let f(x) = x − 3 and g(x) = x + 11. Find f(x) ⋅ g(x).
x2 − 8x − 33
x2 − 8x + 14
x2 + 8x + 14
x2 + 8x − 33
Question 8(Multiple Choice Worth 1 points)
(01.08 MC)
Multiply 5x2(2x2 + 13x − 5).
10x4 + 65x3 − 25x2
10x2 + 65x − 25
7x2 + 18x − 10
7x4 + 18x3 − 10x2
Question 9(Multiple Choice Worth 1 points)
(01.08 MC)
Which of the following represents the area of a rectangle whose length is 3x + 5 and whose width is x − 2?
3x2 − x − 10
3x2 − 10
3x2 + x − 10
3x2 − 11x − 10
Question 10(Multiple Choice Worth 1 points)
(01.08 MC)
Subtract (5x2 + 3) − (2x2 + 4x − 12).
3x2 − 4x + 15
3x2 + 4x + 15
3x2 − 4x − 9
3x2 + 4x − 9
16x2 + 49
16x2 + 28x + 49
16x2 + 56x + 49
8x2 + 14
Question 2(Multiple Choice Worth 1 points)
(01.08 MC)
Multiply (2x2 + 3x − 6)(x − 1).
2x3 + 3x2 − 6x + 6
2x3 − 18x2 − 3x + 6
2x3 − 12x2 + 3x + 6
2x3 + x2 − 9x + 6
Question 3(Multiple Choice Worth 1 points)
(01.08 MC)
Let f(x) = 3x2 + x − 3 and g(x) = x2 − 5x + 1. Find f(x) − g(x).
2x2 − 4x − 2
2x2 − 4x − 4
2x2 + 6x − 2
2x2 + 6x − 4
Question 4(Multiple Choice Worth 1 points)
(01.08 MC)
Let f(x) = x2 + 3x − 4 and g(x) = x + 5. Find f(x) ⋅ g(x).
x3 + 3x2 + 16x − 20
x3 + 5x2 + 14x − 20
x3 + 8x2 + 11x − 20
x3 + 9x2 + 19x − 20
Question 5(Multiple Choice Worth 1 points)
(01.08 MC)
A company makes video games. The price of a video game is modeled by the function p(x) = 30x + 2, where x is the number of years since the company started producing games. The number of video games they sell is modeled by the function s(x) = 500x + 250. To find the total revenue from their video games, the company should use what operation on the polynomials?
Addition
Subtraction
Multiplication
It cannot be determined
Question 6(Multiple Choice Worth 1 points)
(01.08 MC)
Add (3x4 − 2x3 + 1) + (12x4 + x2 − 11).
15x4 − x3 − 10
15x4 − x2 − 10
15x4 − 2x3 + x2 + 10
15x4 − 2x3 + x2 − 10
Question 7(Multiple Choice Worth 1 points)
(01.08 MC)
Let f(x) = x − 3 and g(x) = x + 11. Find f(x) ⋅ g(x).
x2 − 8x − 33
x2 − 8x + 14
x2 + 8x + 14
x2 + 8x − 33
Question 8(Multiple Choice Worth 1 points)
(01.08 MC)
Multiply 5x2(2x2 + 13x − 5).
10x4 + 65x3 − 25x2
10x2 + 65x − 25
7x2 + 18x − 10
7x4 + 18x3 − 10x2
Question 9(Multiple Choice Worth 1 points)
(01.08 MC)
Which of the following represents the area of a rectangle whose length is 3x + 5 and whose width is x − 2?
3x2 − x − 10
3x2 − 10
3x2 + x − 10
3x2 − 11x − 10
Question 10(Multiple Choice Worth 1 points)
(01.08 MC)
Subtract (5x2 + 3) − (2x2 + 4x − 12).
3x2 − 4x + 15
3x2 + 4x + 15
3x2 − 4x − 9
3x2 + 4x − 9
Answers
Answered by
GPT-4o mini
Here are the answers to your questions:
**Question 1: Multiply (4x + 7)².**
- Expanding: \( (4x + 7)(4x + 7) = 16x^2 + 28x + 28x + 49 = 16x^2 + 56x + 49 \)
- **Answer: 16x² + 56x + 49**
---
**Question 2: Multiply (2x² + 3x − 6)(x − 1).**
- Expanding:
- \( 2x² \cdot x = 2x³ \)
- \( 2x² \cdot (-1) = -2x² \)
- \( 3x \cdot x = 3x² \)
- \( 3x \cdot (-1) = -3x \)
- \( -6 \cdot x = -6x \)
- \( -6 \cdot (-1) = 6 \)
Combining them:
\( 2x³ + (3x² - 2x²) + (-3x - 6x) + 6 = 2x³ + x² - 9x + 6 \)
- **Answer: 2x³ + x² − 9x + 6**
---
**Question 3: Let f(x) = 3x² + x − 3 and g(x) = x² − 5x + 1. Find f(x) − g(x).**
- Calculating:
\( f(x) - g(x) = (3x² + x - 3) - (x² - 5x + 1) \)
- This simplifies to:
\( 3x² + x - 3 - x² + 5x - 1 = (3x² - x²) + (x + 5x) + (-3 - 1) \)
- So, \( 2x² + 6x - 4 \)
- **Answer: 2x² + 6x − 4**
---
**Question 4: Let f(x) = x² + 3x − 4 and g(x) = x + 5. Find f(x) ⋅ g(x).**
- Expanding:
\( (x² + 3x - 4)(x + 5) = x²(x) + x²(5) + 3x(x) + 3x(5) - 4(x) - 4(5) \)
- This results in:
\( x³ + 5x² + 3x² + 15x - 4x - 20 = x³ + 8x² + 11x - 20 \)
- **Answer: x³ + 8x² + 11x − 20**
---
**Question 5: A company makes video games. The price of a video game is modeled by the function p(x) = 30x + 2, and the number of video games they sell is modeled by the function s(x) = 500x + 250. To find the total revenue, the company should use what operation on the polynomials?**
- Revenue = Price × Quantity
Thus, the operation should be multiplication.
- **Answer: Multiplication**
---
**Question 6: Add (3x⁴ − 2x³ + 1) + (12x⁴ + x² − 11).**
- Combining:
\( (3x⁴ + 12x⁴) + (-2x³) + (x²) + (1 - 11) = 15x⁴ - 2x³ + x² - 10 \)
- **Answer: 15x⁴ − 2x³ + x² − 10**
---
**Question 7: Let f(x) = x − 3 and g(x) = x + 11. Find f(x) ⋅ g(x).**
- Expanding:
\( (x - 3)(x + 11) = x² + 11x - 3x - 33 = x² + 8x - 33 \)
- **Answer: x² + 8x − 33**
---
**Question 8: Multiply 5x²(2x² + 13x − 5).**
- Expanding:
5x² * 2x² = 10x⁴,
5x² * 13x = 65x³,
5x² * (-5) = -25x².
- Combining gives:
\(10x⁴ + 65x³ - 25x²\)
- **Answer: 10x⁴ + 65x³ − 25x²**
---
**Question 9: Which of the following represents the area of a rectangle, length = 3x + 5, width = x − 2?**
- Area = Length × Width
- Expanding:
\( (3x + 5)(x - 2) = 3x² - 6x + 5x - 10 = 3x² - x - 10 \)
- **Answer: 3x² − x − 10**
---
**Question 10: Subtract (5x² + 3) − (2x² + 4x − 12).**
- This becomes:
\( (5x² + 3) - (2x² + 4x - 12) = 5x² + 3 - 2x² - 4x + 12 \)
- This simplifies to:
\( (5x² - 2x²) + (-4x) + (3 + 12) = 3x² - 4x + 15 \)
- **Answer: 3x² − 4x + 15**
Let me know if you need further assistance!
**Question 1: Multiply (4x + 7)².**
- Expanding: \( (4x + 7)(4x + 7) = 16x^2 + 28x + 28x + 49 = 16x^2 + 56x + 49 \)
- **Answer: 16x² + 56x + 49**
---
**Question 2: Multiply (2x² + 3x − 6)(x − 1).**
- Expanding:
- \( 2x² \cdot x = 2x³ \)
- \( 2x² \cdot (-1) = -2x² \)
- \( 3x \cdot x = 3x² \)
- \( 3x \cdot (-1) = -3x \)
- \( -6 \cdot x = -6x \)
- \( -6 \cdot (-1) = 6 \)
Combining them:
\( 2x³ + (3x² - 2x²) + (-3x - 6x) + 6 = 2x³ + x² - 9x + 6 \)
- **Answer: 2x³ + x² − 9x + 6**
---
**Question 3: Let f(x) = 3x² + x − 3 and g(x) = x² − 5x + 1. Find f(x) − g(x).**
- Calculating:
\( f(x) - g(x) = (3x² + x - 3) - (x² - 5x + 1) \)
- This simplifies to:
\( 3x² + x - 3 - x² + 5x - 1 = (3x² - x²) + (x + 5x) + (-3 - 1) \)
- So, \( 2x² + 6x - 4 \)
- **Answer: 2x² + 6x − 4**
---
**Question 4: Let f(x) = x² + 3x − 4 and g(x) = x + 5. Find f(x) ⋅ g(x).**
- Expanding:
\( (x² + 3x - 4)(x + 5) = x²(x) + x²(5) + 3x(x) + 3x(5) - 4(x) - 4(5) \)
- This results in:
\( x³ + 5x² + 3x² + 15x - 4x - 20 = x³ + 8x² + 11x - 20 \)
- **Answer: x³ + 8x² + 11x − 20**
---
**Question 5: A company makes video games. The price of a video game is modeled by the function p(x) = 30x + 2, and the number of video games they sell is modeled by the function s(x) = 500x + 250. To find the total revenue, the company should use what operation on the polynomials?**
- Revenue = Price × Quantity
Thus, the operation should be multiplication.
- **Answer: Multiplication**
---
**Question 6: Add (3x⁴ − 2x³ + 1) + (12x⁴ + x² − 11).**
- Combining:
\( (3x⁴ + 12x⁴) + (-2x³) + (x²) + (1 - 11) = 15x⁴ - 2x³ + x² - 10 \)
- **Answer: 15x⁴ − 2x³ + x² − 10**
---
**Question 7: Let f(x) = x − 3 and g(x) = x + 11. Find f(x) ⋅ g(x).**
- Expanding:
\( (x - 3)(x + 11) = x² + 11x - 3x - 33 = x² + 8x - 33 \)
- **Answer: x² + 8x − 33**
---
**Question 8: Multiply 5x²(2x² + 13x − 5).**
- Expanding:
5x² * 2x² = 10x⁴,
5x² * 13x = 65x³,
5x² * (-5) = -25x².
- Combining gives:
\(10x⁴ + 65x³ - 25x²\)
- **Answer: 10x⁴ + 65x³ − 25x²**
---
**Question 9: Which of the following represents the area of a rectangle, length = 3x + 5, width = x − 2?**
- Area = Length × Width
- Expanding:
\( (3x + 5)(x - 2) = 3x² - 6x + 5x - 10 = 3x² - x - 10 \)
- **Answer: 3x² − x − 10**
---
**Question 10: Subtract (5x² + 3) − (2x² + 4x − 12).**
- This becomes:
\( (5x² + 3) - (2x² + 4x - 12) = 5x² + 3 - 2x² - 4x + 12 \)
- This simplifies to:
\( (5x² - 2x²) + (-4x) + (3 + 12) = 3x² - 4x + 15 \)
- **Answer: 3x² − 4x + 15**
Let me know if you need further assistance!