Question
Which of the following quadratic equations can be solved by grouping?(1 point)
Responses
x^2−4x−8=0
x^2+8x−22=0
x^2−12x+18=0
x^2+10x+21=0
Responses
x^2−4x−8=0
x^2+8x−22=0
x^2−12x+18=0
x^2+10x+21=0
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To determine which quadratic equation can be solved by grouping, we need to look for an equation where the middle term can be split into two terms that allow factoring by grouping.
1. **\(x^2 - 4x - 8 = 0\)**
- This cannot be factored easily by grouping.
2. **\(x^2 + 8x - 22 = 0\)**
- This cannot be factored easily by grouping.
3. **\(x^2 - 12x + 18 = 0\)**
- The middle term, -12x, does not have factor pairs that neatly allow for grouping.
4. **\(x^2 + 10x + 21 = 0\)**
- This can be factored as \((x + 3)(x + 7) = 0\).
The equation that can be grouped and factored is \(x^2 + 10x + 21 = 0\).
**Answer:** \(x^2 + 10x + 21 = 0\) is the equation that can be solved by grouping.
1. **\(x^2 - 4x - 8 = 0\)**
- This cannot be factored easily by grouping.
2. **\(x^2 + 8x - 22 = 0\)**
- This cannot be factored easily by grouping.
3. **\(x^2 - 12x + 18 = 0\)**
- The middle term, -12x, does not have factor pairs that neatly allow for grouping.
4. **\(x^2 + 10x + 21 = 0\)**
- This can be factored as \((x + 3)(x + 7) = 0\).
The equation that can be grouped and factored is \(x^2 + 10x + 21 = 0\).
**Answer:** \(x^2 + 10x + 21 = 0\) is the equation that can be solved by grouping.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.