Question

Which of the following quadratic equations is not solvable by grouping?(1 point)
Responses

2x2−2x−10=0
2 x squared minus 2 x minus 10 is equal to 0

x2−2x+1=0
x squared minus 2 x plus 1 is equal to 0

2x2+14x+12=0
2 x squared plus 14 x plus 12 is equal to 0

x2−12x+35=0

Answer 1

To determine which of the quadratic equations is not solvable by grouping, we should check if we can factor them into a product of binomials.

1. **Equation: 2x² - 2x - 10 = 0**
- Factor out the common factor: 2(x² - x - 5) = 0
- The quadratic x² - x - 5 does not factor nicely into integers, so this one isn't easily solvable by grouping.

2. **Equation: x² - 2x + 1 = 0**
- This factors as (x - 1)(x - 1) = 0 or (x - 1)² = 0, which is solvable.

3. **Equation: 2x² + 14x + 12 = 0**
- Factor out the common factor: 2(x² + 7x + 6) = 0
- The quadratic x² + 7x + 6 factors as (x + 1)(x + 6) = 0, which is solvable.

4. **Equation: x² - 12x + 35 = 0**
- This factors as (x - 5)(x - 7) = 0, which is solvable.

From this analysis, the quadratic equation **2x² - 2x - 10 = 0** is the one that is not easily solvable by grouping, as it does not factor nicely after extracting the common factor.