Question

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

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

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

x2+10x+21=0

Answer 1

The method of grouping is typically applied when we can factor the quadratic expression into two binomials.

To determine which quadratic equation can be solved by grouping, we generally look for patterns in the coefficients or whether the quadratic can be factored nicely.

1. \(x^2 + 8x - 22 = 0\): The factors of -22 that add up to +8 do not exist. Therefore, it cannot be easily factored by grouping.

2. \(x^2 - 4x - 8 = 0\): The factors of -8 that add up to -4 do not yield nice integers. This does not seem to group well.

3. \(x^2 - 12x + 18 = 0\): The factors of +18 that add up to -12 are not simple. This also would not necessarily lend itself to grouping.

4. \(x^2 + 10x + 21 = 0\): This quadratic can be factored as \((x + 3)(x + 7) = 0\).

Since it’s clear from the above evaluations that the last equation can be factored smoothly into binomials, the answer is:

\(x^2 + 10x + 21 = 0\) can be solved by grouping.