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

Question

Responses

x^2+8x−22=0
x squared plus 8 x minus 22 equals 0

x^2+10x+21=0
x squared plus 10 x plus 21 equals 0

x^2−4x−8=0
x squared minus 4 x minus 8 equals 0

x^2−12x+18=0

Answer 1

To determine which of these quadratic equations can be solved by grouping, we look for quadratic equations that can be factored into a product of two binomials. This typically involves recognizing a common form or being able to rearrange the equation in a way that allows for grouping.

1. \(x^2 + 8x - 22 = 0\)

   • Cannot be easily factored; does not group nicely.

2. \(x^2 + 10x + 21 = 0\)

   • This can be factored as \((x + 3)(x + 7) = 0\) and therefore can be solved easily.

3. \(x^2 - 4x - 8 = 0\)

   • Cannot be factored nicely for grouping; does not rearrange.

4. \(x^2 - 12x + 18 = 0\)

   • This also cannot be factored nicely; does not group.

Conclusion: The quadratic equation that can be solved by grouping is \(x^2 + 10x + 21 = 0\).