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+10x+21=0
x^2−12x+18=0

Answer 1

To determine which quadratic equation can be solved by grouping, we look for a quadratic that can be factored into two binomials by grouping its terms.

Let's analyze each equation:

1. **\(x^2−4x−8=0\)**
- This does not factor nicely into integer factors.

2. **\(x^2+8x−22=0\)**
- This does not factor nicely either.

3. **\(x^2+10x+21=0\)**
- This can be factored as \((x + 3)(x + 7) = 0\), but it is a straightforward factoring rather than grouping.

4. **\(x^2−12x+18=0\)**
- This can potentially be factored by grouping or trial and error but does not yield integer factors.

Of these options, while none clearly suggest grouping in the traditional sense, the quadratic **\(x^2 + 10x + 21 = 0\)** can be factored without grouping, but it still remains the most suitable option because it allows for a straightforward factorization.

So, in conclusion, although none are best suited for grouping, **the option \(x^2 + 10x + 21 = 0\)** is the simplest and adds context for resolution.