Question

Which of the following quadratic equations can be solved by grouping?(1 point) Responses x2−12x+18=0 x squared minus 12 x plus 18 equals 0 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+10x+21=0

Answer 1

To determine which of the given quadratic equations can be solved by grouping, we need to check if the middle term can be split into two terms that allow for a common factor extraction.

1. **\(x^2 - 12x + 18 = 0\)**: The constant term 18 doesn't factor nicely to split -12 into two integers. Not suitable for grouping.

2. **\(x^2 + 8x - 22 = 0\)**: The constant term -22 also doesn't allow for a split of 8 into two factors. Not suitable for grouping.

3. **\(x^2 - 4x - 8 = 0\)**: The constant term -8 could potentially split -4, but it’s not straightforward to find two factors that work. Also, not suitable for grouping.

4. **\(x^2 + 10x + 21 = 0\)**: The middle term 10 can be split into 3 and 7 (since 3 * 7 = 21, and 3 + 7 = 10).

Thus, the equation **\(x^2 + 10x + 21 = 0\)** can be solved by grouping, as it can be written as:

\[
x^2 + 3x + 7x + 21 = 0 \implies x(x + 3) + 7(x + 3) = 0 \implies (x + 3)(x + 7) = 0
\]

So the answer is:

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