Question

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

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

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

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

x2−12x+18=0

Answer 1

To determine which of the given quadratic equations can be solved by grouping, we can look for quadratic equations that can be factored easily into two binomials.

1. **\(x^2 - 4x - 8 = 0\)**: This does not factor nicely using integers, as there are no two numbers that multiply to \(-8\) and add to \(-4\).

2. **\(x^2 + 10x + 21 = 0\)**: This factors nicely as \((x + 3)(x + 7) = 0\). It can be solved by factoring, but it does not require grouping.

3. **\(x^2 + 8x - 22 = 0\)**: To factor this using grouping, we look for two numbers that multiply to \(-22\) and add to \(8\). The numbers \(11\) and \(-2\) work because \(11 \cdot (-2) = -22\) and \(11 - 2 = 9\), so this quadratic can be rewritten and solved by grouping as \(x^2 + 11x - 2x - 22 = 0\).

4. **\(x^2 - 12x + 18 = 0\)**: This does not factor neatly using integers, as there are no two numbers that multiply to \(18\) and add to \(-12\).

Among the options, \(x^2 + 8x - 22 = 0\) can be solved by grouping after finding suitable pairs for factoring, making it the appropriate choice for this method.

**Therefore, the quadratic equation that can be solved by grouping is:**

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