Question
Given the following perfect square trinomial, find the missing term:
___x2 + 40x + 100
1
2
4
10
Question 2(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 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 4x2 + 28x + 49 square feet, what is the length of one side of the room?
(7x + 2) feet
(2x + 7) feet
(2x − 7) feet
(7x − 2) feet
Question 4(Multiple Choice Worth 1 points)
(07.03 LC)
Factor completely x2 − 10x + 25.
(x − 5)(x − 5)
(x + 5)(x + 5)
(x + 5)(x − 5)
(x − 25)(x − 1)
Question 5(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 6(Multiple Choice Worth 1 points)
(07.03 MC)
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 7(Multiple Choice Worth 1 points)
(07.03 MC)
Factor completely 8x2 − 4x − 84.
4(2x − 3)(x + 7)
4(2x + 3)(x − 7)
4(x − 3)(2x + 7)
4(x + 3)(2x − 7)
Question 8(Multiple Choice Worth 1 points)
(07.03 MC)
Factor completely 16x2 + 40x + 25.
(4x − 5)(4x − 5)
(2x − 5)(2x − 5)
(2x + 5)(2x + 5)
(4x + 5)(4x + 5)
Question 9(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 10(Multiple Choice Worth 1 points)
(07.03 MC)
Factor completely 3x2 − 11x + 8.
(x + 4)(3x − 2)
(x − 2)(3x − 4)
(x + 1)(3x − 8)
(x − 1)(3x − 8)
___x2 + 40x + 100
1
2
4
10
Question 2(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 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 4x2 + 28x + 49 square feet, what is the length of one side of the room?
(7x + 2) feet
(2x + 7) feet
(2x − 7) feet
(7x − 2) feet
Question 4(Multiple Choice Worth 1 points)
(07.03 LC)
Factor completely x2 − 10x + 25.
(x − 5)(x − 5)
(x + 5)(x + 5)
(x + 5)(x − 5)
(x − 25)(x − 1)
Question 5(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 6(Multiple Choice Worth 1 points)
(07.03 MC)
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 7(Multiple Choice Worth 1 points)
(07.03 MC)
Factor completely 8x2 − 4x − 84.
4(2x − 3)(x + 7)
4(2x + 3)(x − 7)
4(x − 3)(2x + 7)
4(x + 3)(2x − 7)
Question 8(Multiple Choice Worth 1 points)
(07.03 MC)
Factor completely 16x2 + 40x + 25.
(4x − 5)(4x − 5)
(2x − 5)(2x − 5)
(2x + 5)(2x + 5)
(4x + 5)(4x + 5)
Question 9(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 10(Multiple Choice Worth 1 points)
(07.03 MC)
Factor completely 3x2 − 11x + 8.
(x + 4)(3x − 2)
(x − 2)(3x − 4)
(x + 1)(3x − 8)
(x − 1)(3x − 8)
Answers
GPT-4o mini
Let's tackle the questions one by one.
### Question 1
For the trinomial: ___x² + 40x + 100
A perfect square trinomial takes the form \((ax + b)^2\) where the middle term is \(2ab\) and the last term is \(b^2\).
Here, \(40 = 2ab\). So, we find \(b\) by solving \(b = 40/(2a)\).
In this case, since we are looking for \(b²\):
- The last term is \(100\), which is \(b^2\). Therefore:
- \(b = √100 = 10\).
Thus, \(b = 10\).
So, the missing term is **10**.
### Question 2
Select the polynomial that is a perfect square trinomial.
- **36x² − 4x + 16** (not a perfect square since the middle term is not twice the product of the square roots of the other two terms).
- **16x² − 8x + 36** (not a perfect square).
- **25x² + 9x + 4** (not a perfect square).
- **4x² + 20x + 25** (this is \((2x + 5)^2\)).
So, the correct answer is **4x² + 20x + 25**.
### Question 3
Rhett's area of the room: \(4x² + 28x + 49\).
Let's factor \(4x² + 28x + 49\):
1. \(= (2x + 7)²\)
Thus, the length of one side of the room is **(2x + 7) feet**.
### Question 4
Factor completely: \(x² − 10x + 25\).
This is a perfect square trinomial:
- \(= (x - 5)(x - 5)\) or \((x - 5)²\)
So, the answer is **(x − 5)(x − 5)**.
### Question 5
Factor completely: \(3x² + 5x + 1\).
To factor this, we can look for two numbers that multiply to \(3 \times 1 = 3\) and add up to \(5\). The correct factorization is:
\(= (3x + 1)(x + 1)\).
So, the answer is **(3x + 1)(x + 1)**.
### Question 6
For \(2x² − 12xy − 32y² = 2(x - 8y)(x + By)\):
To find \(B\), we can match the coefficients:
- The term that would arise from \(-8y\) would yield \(B\) to satisfy \(-12y\).
- Thus, we have \(B = -4\).
So, the answer is **−4**.
### Question 7
Factor completely: \(8x² − 4x − 84\).
First, factor out the common factor of \(4\):
- \(= 4(2x² - x - 21)\).
Now we factor \(2x² - x - 21\):
- This factors to \( (2x + 7)(x - 3) \).
Combining:
- \(= 4(2x + 7)(x - 3)\).
So, the answer is **4(2x − 3)(x + 7)**.
### Question 8
Factor completely: \(16x² + 40x + 25\).
This is another perfect square:
- \(= (4x + 5)^2\).
The answer is **(4x + 5)(4x + 5)**.
### Question 9
Factor completely: \(2x² + 9x + 4\).
We look for two numbers that multiply to \(2 \times 4 = 8\) and add up to \(9\). The correct factorization is:
- \(= (2x + 1)(x + 4)\).
So, the answer is **(2x + 1)(x + 4)**.
### Question 10
Factor completely: \(3x² − 11x + 8\).
We look for factors that multiply to \(3 \times 8 = 24\) and add up to \(-11\). The correct factorization is:
- \(= (x - 8)(3x - 1)\).
So, the answer is **(x − 8)(3x − 1)**.
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These are the answers to all the questions!
### Question 1
For the trinomial: ___x² + 40x + 100
A perfect square trinomial takes the form \((ax + b)^2\) where the middle term is \(2ab\) and the last term is \(b^2\).
Here, \(40 = 2ab\). So, we find \(b\) by solving \(b = 40/(2a)\).
In this case, since we are looking for \(b²\):
- The last term is \(100\), which is \(b^2\). Therefore:
- \(b = √100 = 10\).
Thus, \(b = 10\).
So, the missing term is **10**.
### Question 2
Select the polynomial that is a perfect square trinomial.
- **36x² − 4x + 16** (not a perfect square since the middle term is not twice the product of the square roots of the other two terms).
- **16x² − 8x + 36** (not a perfect square).
- **25x² + 9x + 4** (not a perfect square).
- **4x² + 20x + 25** (this is \((2x + 5)^2\)).
So, the correct answer is **4x² + 20x + 25**.
### Question 3
Rhett's area of the room: \(4x² + 28x + 49\).
Let's factor \(4x² + 28x + 49\):
1. \(= (2x + 7)²\)
Thus, the length of one side of the room is **(2x + 7) feet**.
### Question 4
Factor completely: \(x² − 10x + 25\).
This is a perfect square trinomial:
- \(= (x - 5)(x - 5)\) or \((x - 5)²\)
So, the answer is **(x − 5)(x − 5)**.
### Question 5
Factor completely: \(3x² + 5x + 1\).
To factor this, we can look for two numbers that multiply to \(3 \times 1 = 3\) and add up to \(5\). The correct factorization is:
\(= (3x + 1)(x + 1)\).
So, the answer is **(3x + 1)(x + 1)**.
### Question 6
For \(2x² − 12xy − 32y² = 2(x - 8y)(x + By)\):
To find \(B\), we can match the coefficients:
- The term that would arise from \(-8y\) would yield \(B\) to satisfy \(-12y\).
- Thus, we have \(B = -4\).
So, the answer is **−4**.
### Question 7
Factor completely: \(8x² − 4x − 84\).
First, factor out the common factor of \(4\):
- \(= 4(2x² - x - 21)\).
Now we factor \(2x² - x - 21\):
- This factors to \( (2x + 7)(x - 3) \).
Combining:
- \(= 4(2x + 7)(x - 3)\).
So, the answer is **4(2x − 3)(x + 7)**.
### Question 8
Factor completely: \(16x² + 40x + 25\).
This is another perfect square:
- \(= (4x + 5)^2\).
The answer is **(4x + 5)(4x + 5)**.
### Question 9
Factor completely: \(2x² + 9x + 4\).
We look for two numbers that multiply to \(2 \times 4 = 8\) and add up to \(9\). The correct factorization is:
- \(= (2x + 1)(x + 4)\).
So, the answer is **(2x + 1)(x + 4)**.
### Question 10
Factor completely: \(3x² − 11x + 8\).
We look for factors that multiply to \(3 \times 8 = 24\) and add up to \(-11\). The correct factorization is:
- \(= (x - 8)(3x - 1)\).
So, the answer is **(x − 8)(3x − 1)**.
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These are the answers to all the questions!