To determine which of the quadratic equations can be solved by grouping, we need to factor the quadratic expressions and see if we can group them into factors.
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\(x^2 - 4x - 8 = 0\)
This does not factor nicely for grouping. -
\(x^2 + 8x - 22 = 0\)
This also does not factor nicely for grouping. -
\(x^2 + 10x + 21 = 0\)
This can be factored as \((x + 3)(x + 7) = 0\), which does not require grouping. -
\(x^2 - 12x + 18 = 0\)
This can be rewritten as \(x^2 - 12x + 36 - 18 = 0\) or \((x - 6)^2 - 18 = 0\), but it's not suitable for direct grouping either.
After reviewing the equations, it seems that none of the equations can be solved by grouping. However, the equation \(x^2 + 10x + 21 = 0\) is the easiest to factor but does not fall strictly under grouping methods (it uses standard factoring).
If you're looking specifically for those that could potentially use grouping in a broader sense, look for numbers that split to create two pairs, but in general terms here none stand exclusively for grouping.
So, it can be said that none of these quadratic equations strictly can be solved using the grouping method unless further context of grouping is provided. If forced to choose, \(x^2 + 10x + 21 = 0\) is an easy factorization.