Question

Which of the following quadratic equations is not solvable by grouping?(1 point) Responses x2−2x+1=0 x squared minus 2 x plus 1 equals 0 2x2−2x−10=0 2 x squared minus 2 x minus 10 equals 0 2x2+14x+12=0 2 x squared plus 14 x plus 12 equals 0 x2−12x+35=0

Answer 1

To determine which of the given quadratic equations is not solvable by grouping, we should consider their forms.

1. \( x^2 - 2x + 1 = 0 \)
2. \( 2x^2 - 2x - 10 = 0 \)
3. \( 2x^2 + 14x + 12 = 0 \)
4. \( x^2 - 12x + 35 = 0 \)

**Grouping Method:** This method involves rearranging and factoring the equation. Typically, it works well when the quadratic can be expressed in a way that allows us to group terms conveniently.

We'll start by analyzing each equation:

1. **\( x^2 - 2x + 1 = 0 \)**
- This factors easily as \( (x-1)^2 = 0 \).

2. **\( 2x^2 - 2x - 10 = 0 \)**
- Divide through by 2 to get \( x^2 - x - 5 = 0 \). This does not factor nicely, but it can be solved by completing the square or using the quadratic formula.

3. **\( 2x^2 + 14x + 12 = 0 \)**
- This can be factored as \( 2(x^2 + 7x + 6) = 0 \) and further factored as \( 2(x+6)(x+1) = 0 \), which can be grouped.

4. **\( x^2 - 12x + 35 = 0 \)**
- This factors to \( (x-5)(x-7) = 0 \), which can also be solved by grouping.

From this analysis, while all equations can be solved using various methods, the equation \( 2x^2 - 2x - 10 = 0 \) does not lend itself to “solving by grouping” because it requires simplification before any grouping strategies are applied.

Thus, **the quadratic equation that is not solvable by grouping is:**
**\( 2x^2 - 2x - 10 = 0 \)**.