To determine which of the given quadratic equations can be solved by grouping, we need to look for a way to factor each equation.
Let's analyze each option:
A. \( x^2 - 12x + 18 = 0 \)
This can be factored as: \( (x - 6)(x - 3) = 0 \) No grouping is necessary.
B. \( x^2 + 8x - 22 = 0 \)
We look for factors of \(-22\) that add up to \(8\). The factors \(11\) and \(-2\) work: \( (x + 11)(x - 2) = 0 \) No grouping is necessary.
C. \( x^2 - 4x - 8 = 0 \)
We can try to factor by grouping:
- Rearranging gives \( x^2 - 4x + 8 = 0 \).
- Checking for combinations that yield \(-8\) with a middle term of \(-4\) does not yield integer factors.
D. \( x^2 + 10x + 21 = 0 \)
This can be factored as: \( (x + 3)(x + 7) = 0 \) No grouping is necessary.
Conclusion: None of the quadratic equations listed can be solved by grouping. However, if we reinterpret the problem, grouping is typically used for simpler quadratics where you can rearrange terms into two separate binomials. Here, each equation can be factored directly. If you seek the "best fit" option for grouping, typically that would be option C (since it leads you back toward rearranging).
But strictly speaking, according to typical grouping techniques, none fit that criteria.