Question
Given the trinomial, what is the value of the coefficient B in the factored form?
2x2 − 12xy − 32y2 = 2(x − 8y)(x + By)
−4
−2
2
4
Question 2(Multiple Choice Worth 1 points)
(07.03 MC)
Factor completely 3x2 + 5x + 1.
(3x + 1)(x + 1)
(3x + 5)(x + 1)
(3x − 5)(x + 1)
Prime
Question 3(Multiple Choice Worth 1 points)
(07.03 MC)
Rhett decides to build a square room for his movie and music collection. If the area of the room is 9x2 − 6x + 1 square feet, what is the length of one side of the room?
(3x + 1) feet
(9x − 1) feet
(3x − 1) feet
(9x + 1) feet
Question 4(Multiple Choice Worth 1 points)
(07.03 MC)
Factor completely 9x2 + 42x + 49.
(3x + 7)(3x − 7)
(9x − 7)(9x − 7)
(3x + 7)(3x + 7)
(9x + 7)(9x + 7)
Question 5(Multiple Choice Worth 1 points)
(07.03 MC)
Factor completely 18x2 − 21x −15.
3(2x + 1)(3x − 5)
3(2x − 5)(3x + 1)
3(2x − 1)(3x + 5)
3(6x + 1)(x − 5)
Question 6(Multiple Choice Worth 1 points)
(07.03 MC)
Given the following perfect square trinomial, find the missing term:
4x2 + ___x + 49
7
14
28
36
Question 7(Multiple Choice Worth 1 points)
(07.03 MC)
Factor completely 2x2 + 9x + 4.
(2x + 2)(x + 2)
(2x + 1)(x + 4)
(2x + 4)(x + 1)
(2x + 2)(x + 4)
Question 8(Multiple Choice Worth 1 points)
(07.03 LC)
Select the polynomial that is a perfect square trinomial.
36x2 − 4x + 16
16x2 − 8x + 36
25x2 + 9x + 4
4x2 + 20x + 25
Question 9(Multiple Choice Worth 1 points)
(07.03 LC)
Factor completely x2 − 8x + 16.
(x + 4)(x + 4)
(x − 4)(x − 4)
(x + 4)(x − 4)
(x − 2)(x − 8)
Question 10(Multiple Choice Worth 1 points)
(07.03 MC)
Factor completely 3x2 + 2x − 1.
(3x + 1)(x − 1)
(3x + 1)(x + 1)
(3x − 1)(x + 1)
(3x − 1)(x − 1)
2x2 − 12xy − 32y2 = 2(x − 8y)(x + By)
−4
−2
2
4
Question 2(Multiple Choice Worth 1 points)
(07.03 MC)
Factor completely 3x2 + 5x + 1.
(3x + 1)(x + 1)
(3x + 5)(x + 1)
(3x − 5)(x + 1)
Prime
Question 3(Multiple Choice Worth 1 points)
(07.03 MC)
Rhett decides to build a square room for his movie and music collection. If the area of the room is 9x2 − 6x + 1 square feet, what is the length of one side of the room?
(3x + 1) feet
(9x − 1) feet
(3x − 1) feet
(9x + 1) feet
Question 4(Multiple Choice Worth 1 points)
(07.03 MC)
Factor completely 9x2 + 42x + 49.
(3x + 7)(3x − 7)
(9x − 7)(9x − 7)
(3x + 7)(3x + 7)
(9x + 7)(9x + 7)
Question 5(Multiple Choice Worth 1 points)
(07.03 MC)
Factor completely 18x2 − 21x −15.
3(2x + 1)(3x − 5)
3(2x − 5)(3x + 1)
3(2x − 1)(3x + 5)
3(6x + 1)(x − 5)
Question 6(Multiple Choice Worth 1 points)
(07.03 MC)
Given the following perfect square trinomial, find the missing term:
4x2 + ___x + 49
7
14
28
36
Question 7(Multiple Choice Worth 1 points)
(07.03 MC)
Factor completely 2x2 + 9x + 4.
(2x + 2)(x + 2)
(2x + 1)(x + 4)
(2x + 4)(x + 1)
(2x + 2)(x + 4)
Question 8(Multiple Choice Worth 1 points)
(07.03 LC)
Select the polynomial that is a perfect square trinomial.
36x2 − 4x + 16
16x2 − 8x + 36
25x2 + 9x + 4
4x2 + 20x + 25
Question 9(Multiple Choice Worth 1 points)
(07.03 LC)
Factor completely x2 − 8x + 16.
(x + 4)(x + 4)
(x − 4)(x − 4)
(x + 4)(x − 4)
(x − 2)(x − 8)
Question 10(Multiple Choice Worth 1 points)
(07.03 MC)
Factor completely 3x2 + 2x − 1.
(3x + 1)(x − 1)
(3x + 1)(x + 1)
(3x − 1)(x + 1)
(3x − 1)(x − 1)
Answers
GPT-4o mini
Here are the answers to each question:
**Question 1**: Given the trinomial \(2x^2 - 12xy - 32y^2 = 2(x - 8y)(x + By)\), we need to find the value of \(B\).
Start with the factorization:
\[
2(x - 8y)(x + By)
\]
Expanding it gives:
\[
2 \left( x^2 + Byx - 8yx - 8By^2 \right) = 2x^2 + 2(By - 8)xy - 16By^2
\]
We need this to match:
\[
2x^2 - 12xy - 32y^2
\]
From comparing coefficients:
- The coefficient of \(xy\) gives:
\[
2(By - 8) = -12 \implies By - 8 = -6 \implies By = 2 \implies B = \frac{2}{y} \text{ (need a specific value of y for B)}
\]
But to proceed normally:
Since we need the constant term of \(-32y^2\) implies:
\[
-16B = -32 \implies B = 2
\]
**B = 2**
---
**Question 2**: Factor completely \(3x^2 + 5x + 1\).
To factor \(3x^2 + 5x + 1\), we can check the factors:
The product of \(3*1 = 3\) and sum \(5\):
The factors \(3\) and \(1\) work,
So we can write this as:
\[
(3x + 1)(x + 1)
\]
**Answer**: \((3x + 1)(x + 1)\)
---
**Question 3**: If the area of the room is \(9x^2 - 6x + 1\), we recognize it as a perfect square.
\[
(3x - 1)^2 \Rightarrow \text{therefore length of one side is } (3x - 1) \text{ feet}
\]
**Answer**: \((3x - 1)\) feet
---
**Question 4**: Factor completely \(9x^2 + 42x + 49\).
Recognizing as a perfect square trinomial:
\[
(3x + 7)(3x + 7) = (3x + 7)^2
\]
**Answer**: \((3x + 7)(3x + 7)\)
---
**Question 5**: Factor \(18x^2 - 21x -15\).
Extracting the GCF which is \(3\):
\[
3(6x^2 - 7x - 5)
\]
Now factoring \(6x^2 - 7x - 5\):
The factors of \(-30\) (6 * -5) that add to -7 are -10 and 3:
\[
3(2x + 1)(3x - 5)
\]
**Answer**: \(3(2x + 1)(3x - 5)\)
---
**Question 6**: Find the missing term in \(4x^2 + \_\_ x + 49\).
Recognizing it as a perfect square trinomial:
The coefficient must be \(2ab\):
\(4x^2 + 28x + 49 = (2x + 7)^2\),
Hence the middle term is \(28\).
**Answer**: \(28\)
---
**Question 7**: Factor \(2x^2 + 9x + 4\).
Trying the factoring method:
The factors are:
\[
(2x + 1)(x + 4)
\]
**Answer**: \((2x + 1)(x + 4)\)
---
**Question 8**: Identify the perfect square trinomial.
Calculating each:
For \(4x^2 + 20x + 25: (2x + 5)^2\), so this is a perfect square trinomial.
**Answer**: \(4x^2 + 20x + 25\)
---
**Question 9**: Factor completely \(x^2 - 8x + 16\).
Recognizing as:
\[
(x - 4)(x - 4) = (x - 4)^2
\]
**Answer**: \((x - 4)(x - 4)\)
---
**Question 10**: Factor \(3x^2 + 2x - 1\).
Looking for two numbers that multiply to \(-3\) and add to \(2\):
Checking the combinations, we find:
\[
(3x - 1)(x + 1)
\]
**Answer**: \((3x - 1)(x + 1)\)
**Question 1**: Given the trinomial \(2x^2 - 12xy - 32y^2 = 2(x - 8y)(x + By)\), we need to find the value of \(B\).
Start with the factorization:
\[
2(x - 8y)(x + By)
\]
Expanding it gives:
\[
2 \left( x^2 + Byx - 8yx - 8By^2 \right) = 2x^2 + 2(By - 8)xy - 16By^2
\]
We need this to match:
\[
2x^2 - 12xy - 32y^2
\]
From comparing coefficients:
- The coefficient of \(xy\) gives:
\[
2(By - 8) = -12 \implies By - 8 = -6 \implies By = 2 \implies B = \frac{2}{y} \text{ (need a specific value of y for B)}
\]
But to proceed normally:
Since we need the constant term of \(-32y^2\) implies:
\[
-16B = -32 \implies B = 2
\]
**B = 2**
---
**Question 2**: Factor completely \(3x^2 + 5x + 1\).
To factor \(3x^2 + 5x + 1\), we can check the factors:
The product of \(3*1 = 3\) and sum \(5\):
The factors \(3\) and \(1\) work,
So we can write this as:
\[
(3x + 1)(x + 1)
\]
**Answer**: \((3x + 1)(x + 1)\)
---
**Question 3**: If the area of the room is \(9x^2 - 6x + 1\), we recognize it as a perfect square.
\[
(3x - 1)^2 \Rightarrow \text{therefore length of one side is } (3x - 1) \text{ feet}
\]
**Answer**: \((3x - 1)\) feet
---
**Question 4**: Factor completely \(9x^2 + 42x + 49\).
Recognizing as a perfect square trinomial:
\[
(3x + 7)(3x + 7) = (3x + 7)^2
\]
**Answer**: \((3x + 7)(3x + 7)\)
---
**Question 5**: Factor \(18x^2 - 21x -15\).
Extracting the GCF which is \(3\):
\[
3(6x^2 - 7x - 5)
\]
Now factoring \(6x^2 - 7x - 5\):
The factors of \(-30\) (6 * -5) that add to -7 are -10 and 3:
\[
3(2x + 1)(3x - 5)
\]
**Answer**: \(3(2x + 1)(3x - 5)\)
---
**Question 6**: Find the missing term in \(4x^2 + \_\_ x + 49\).
Recognizing it as a perfect square trinomial:
The coefficient must be \(2ab\):
\(4x^2 + 28x + 49 = (2x + 7)^2\),
Hence the middle term is \(28\).
**Answer**: \(28\)
---
**Question 7**: Factor \(2x^2 + 9x + 4\).
Trying the factoring method:
The factors are:
\[
(2x + 1)(x + 4)
\]
**Answer**: \((2x + 1)(x + 4)\)
---
**Question 8**: Identify the perfect square trinomial.
Calculating each:
For \(4x^2 + 20x + 25: (2x + 5)^2\), so this is a perfect square trinomial.
**Answer**: \(4x^2 + 20x + 25\)
---
**Question 9**: Factor completely \(x^2 - 8x + 16\).
Recognizing as:
\[
(x - 4)(x - 4) = (x - 4)^2
\]
**Answer**: \((x - 4)(x - 4)\)
---
**Question 10**: Factor \(3x^2 + 2x - 1\).
Looking for two numbers that multiply to \(-3\) and add to \(2\):
Checking the combinations, we find:
\[
(3x - 1)(x + 1)
\]
**Answer**: \((3x - 1)(x + 1)\)