Question

Which of the following quadratic equations can be solved by grouping?(1 point)
Responses

x2+8x−22=0
x squared plus 8 x minus 22 equals 0

x2−12x+18=0
x squared minus 12 x plus 18 equals 0

x2+10x+21=0
x squared plus 10 x plus 21 equals 0

x2−4x−8=0

Answer 1

To determine which of the given quadratic equations can be solved by grouping, we need to look for a quadratic equation that can be factored into two binomials where the middle term can be expressed as a sum of two terms.

1. **\(x^2 + 8x - 22 = 0\)**: This does not factor neatly into a product of binomials, and grouping would not be straightforward.

2. **\(x^2 - 12x + 18 = 0\)**: This also does not factor nicely using grouping.

3. **\(x^2 + 10x + 21 = 0\)**: This can be factored as \( (x + 3)(x + 7) = 0\), but there is no need for grouping here; it's simply factoring, but it does not utilize the grouping method.

4. **\(x^2 - 4x - 8 = 0\)**: Rewriting it as \( x^2 - 4x + 4 - 12 = 0 \), we get \( (x - 2)^2 - 12 = 0 \), which can be solved more easily by completing the square or factoring directly; however, it requires manipulation similar to grouping.

Of all the options, none of them straightforwardly fit the grouping method, but **\(x^2 - 4x - 8 = 0\)** may lead to a more complex problem that can involve grouping indirectly.

The best candidate is generally considered to be:

**\(x^2 - 4x - 8 = 0\)** since you can rearrange or manipulate it in a way that resembles grouping.