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

Question

Responses

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

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

x2−4x−8=0
x squared minus 4 x minus 8 equals 0

x2−12x+18=0

Answer 1

To determine which quadratic equations can be solved by grouping, we look for factors of the quadratic that can be grouped together.

1. \(x^2 + 8x - 22 = 0\): This does not factor nicely for grouping since it does not produce simple integer factors.

2. \(x^2 + 10x + 21 = 0\): This factors nicely as \((x + 3)(x + 7) = 0\). However, it can also be solved by observation without needing to group.

3. \(x^2 - 4x - 8 = 0\): This does not produce factors easily and doesn’t lend itself well to grouping.

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

In conclusion, none of these equations can specifically be classified as easily solved by grouping. However, \(x^2 + 10x + 21 = 0\) can be solved through factoring, but it's not the classic case of "solving by grouping."

If you’re looking for the best candidate from the list for grouping, I would say none fit perfectly, but the simplest form of factoring appears in \(x^2 + 10x + 21 = 0\).