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

Question

Responses

x^2−4x−8=0

x^2+8x−22=0

x^2−12x+18=0

x^2+10x+21=0

Answer 1

To determine which quadratic equation can be solved by grouping, we need to look for an equation where the middle term can be split into two terms that allow factoring by grouping.

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

   • This cannot be factored easily by grouping.

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

   • This cannot be factored easily by grouping.

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

   • The middle term, -12x, does not have factor pairs that neatly allow for grouping.

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

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

The equation that can be grouped and factored is \(x^2 + 10x + 21 = 0\).

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