Question
Question 1(Multiple Choice Worth 2 points)
(02.02 MC)
Select one of the factors of 5x2 + 7x + 2.
(5x − 2)
(x + 2)
(5x + 1)
None of the above
Question 2(Multiple Choice Worth 2 points)
(02.02 MC)
Select one of the factors of x3y2+ 8xy2 + 5x2 + 40.
(xy2 + 5)
(x2 + 4)
(xy2 − 5)
(x2 − 8)
Question 3(Multiple Choice Worth 2 points)
(02.02 MC)
Which of the following expressions is equivalent to ab2 + 6ab + 7a3 – 14a?
(b + 7)(b + 6)(a2 – 2)
b(b + 6) + 7(a2 – 2)
a[b(b + 6) + 7(a2 – 2)]
a[(b + 7)(b + 6)(a2 – 2)]
Question 4(Multiple Choice Worth 2 points)
(02.02 MC)
Select one of the factors of 4x2 + 5x − 6.
(x − 3)
(4x − 3)
(4x + 2)
(x + 6)
Question 5(Multiple Choice Worth 2 points)
(02.02 MC)
Given the polynomial expression 3x2 + 3bx − 6x − 6b, factor completely.
(3x – 6)(x – b)
(x – 2)(x + b)
3(x – 2)(x + b)
3(x + 2)(x + b)
(02.02 MC)
Select one of the factors of 5x2 + 7x + 2.
(5x − 2)
(x + 2)
(5x + 1)
None of the above
Question 2(Multiple Choice Worth 2 points)
(02.02 MC)
Select one of the factors of x3y2+ 8xy2 + 5x2 + 40.
(xy2 + 5)
(x2 + 4)
(xy2 − 5)
(x2 − 8)
Question 3(Multiple Choice Worth 2 points)
(02.02 MC)
Which of the following expressions is equivalent to ab2 + 6ab + 7a3 – 14a?
(b + 7)(b + 6)(a2 – 2)
b(b + 6) + 7(a2 – 2)
a[b(b + 6) + 7(a2 – 2)]
a[(b + 7)(b + 6)(a2 – 2)]
Question 4(Multiple Choice Worth 2 points)
(02.02 MC)
Select one of the factors of 4x2 + 5x − 6.
(x − 3)
(4x − 3)
(4x + 2)
(x + 6)
Question 5(Multiple Choice Worth 2 points)
(02.02 MC)
Given the polynomial expression 3x2 + 3bx − 6x − 6b, factor completely.
(3x – 6)(x – b)
(x – 2)(x + b)
3(x – 2)(x + b)
3(x + 2)(x + b)
Answers
Answered by
GPT-4o mini
Let's go through each question one by one.
**Question 1:**
To factor the polynomial \(5x^2 + 7x + 2\), we can use the method of factoring by grouping or simply check each option.
- Testing \(5x - 2\):
\[
(5x - 2)(x + 1) = 5x^2 + 5x - 2x - 2 = 5x^2 + 3x - 2 \quad (\text{not a factor})
\]
- Testing \(x + 2\):
\[
\text{Not appropriate here as it's a linear term leading to a quadratic on multiplication.}
\]
- Testing \(5x + 1\):
\[
(5x + 1)(x + 2) = 5x^2 + 10x + x + 2 = 5x^2 + 11x + 2 \quad (\text{not a factor})
\]
Hence, **None of the above** is correct.
**Question 2:**
Let's factor \(x^3y^2 + 8xy^2 + 5x^2 + 40\).
- Testing \(xy^2 + 5\):
\[
\text{Not appropriate directly without checking other forms.}
\]
- Testing \(x^2 + 4\):
\[
\text{Again, not appropriate.}
\]
- Testing \(xy^2 - 5\) and \(x^2 - 8\) also mostly leads to invalid pairings.
The valid factor should encapsulate the terms but does not appear among the options.
Thus, the best answer here seems to be **None of the above**.
**Question 3:**
To simplify \(ab^2 + 6ab + 7a^3 - 14a\):
The polynomial can be rearranged:
\[
ab^2 + 6ab + 7a^3 - 14a = a(b^2 + 6b + 7a^2 - 14)
\]
Let's check possible answer calculations:
- Evaluating the option \(b(b + 6) + 7(a^2 - 2)\):
\[
= b^2 + 6b + 7a^2 - 14 \quad (\text{matches with the polynomial})
\]
Thus, the correct answer is \(b(b + 6) + 7(a^2 - 2)\).
**Question 4:**
For \(4x^2 + 5x - 6\), we can factor by trial:
Testing with \(x - 3\),
\[
(4x - 3)(x + 2) = 4x^2 + 8x - 3x - 6 = 4x^2 + 5x - 6 \quad (\text{correct factor})
\]
Thus, the correct answer is \(4x - 3\).
**Question 5:**
Factor \(3x^2 + 3bx - 6x - 6b\):
Rearranging,
\[
3x^2 + (3b - 6)x - 6b
\]
Checking potential choices,
\[
3(x^2 + (b-2)x - 2b) \quad
\text{which leads to options revealing, hence collecting}
\]
The valid option on checking should be:
\[
3(x - 2)(x + b) \quad (\text{leads to relevant ends})
\]
Thus, the answer is \(3(x - 2)(x + b)\).
**Summary of Answers:**
1. None of the above
2. None of the above
3. b(b + 6) + 7(a^2 - 2)
4. (4x - 3)
5. 3(x - 2)(x + b)
**Question 1:**
To factor the polynomial \(5x^2 + 7x + 2\), we can use the method of factoring by grouping or simply check each option.
- Testing \(5x - 2\):
\[
(5x - 2)(x + 1) = 5x^2 + 5x - 2x - 2 = 5x^2 + 3x - 2 \quad (\text{not a factor})
\]
- Testing \(x + 2\):
\[
\text{Not appropriate here as it's a linear term leading to a quadratic on multiplication.}
\]
- Testing \(5x + 1\):
\[
(5x + 1)(x + 2) = 5x^2 + 10x + x + 2 = 5x^2 + 11x + 2 \quad (\text{not a factor})
\]
Hence, **None of the above** is correct.
**Question 2:**
Let's factor \(x^3y^2 + 8xy^2 + 5x^2 + 40\).
- Testing \(xy^2 + 5\):
\[
\text{Not appropriate directly without checking other forms.}
\]
- Testing \(x^2 + 4\):
\[
\text{Again, not appropriate.}
\]
- Testing \(xy^2 - 5\) and \(x^2 - 8\) also mostly leads to invalid pairings.
The valid factor should encapsulate the terms but does not appear among the options.
Thus, the best answer here seems to be **None of the above**.
**Question 3:**
To simplify \(ab^2 + 6ab + 7a^3 - 14a\):
The polynomial can be rearranged:
\[
ab^2 + 6ab + 7a^3 - 14a = a(b^2 + 6b + 7a^2 - 14)
\]
Let's check possible answer calculations:
- Evaluating the option \(b(b + 6) + 7(a^2 - 2)\):
\[
= b^2 + 6b + 7a^2 - 14 \quad (\text{matches with the polynomial})
\]
Thus, the correct answer is \(b(b + 6) + 7(a^2 - 2)\).
**Question 4:**
For \(4x^2 + 5x - 6\), we can factor by trial:
Testing with \(x - 3\),
\[
(4x - 3)(x + 2) = 4x^2 + 8x - 3x - 6 = 4x^2 + 5x - 6 \quad (\text{correct factor})
\]
Thus, the correct answer is \(4x - 3\).
**Question 5:**
Factor \(3x^2 + 3bx - 6x - 6b\):
Rearranging,
\[
3x^2 + (3b - 6)x - 6b
\]
Checking potential choices,
\[
3(x^2 + (b-2)x - 2b) \quad
\text{which leads to options revealing, hence collecting}
\]
The valid option on checking should be:
\[
3(x - 2)(x + b) \quad (\text{leads to relevant ends})
\]
Thus, the answer is \(3(x - 2)(x + b)\).
**Summary of Answers:**
1. None of the above
2. None of the above
3. b(b + 6) + 7(a^2 - 2)
4. (4x - 3)
5. 3(x - 2)(x + b)