Question

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

x2−12x+35=0
x squared minus 12 x plus 35 equals 0

x2−2x+1=0
x squared minus 2 x plus 1 equals 0

2x2+14x+12=0
2 x squared plus 14 x plus 12 equals 0

2x^2−2x−10=0

Answer 1

To determine which of the quadratic equations is not solvable by grouping, we can analyze each equation to see if it can be factored using the method of grouping.

1. **\(x^2 - 12x + 35 = 0\)**: This can be factored as \((x - 5)(x - 7) = 0\).

2. **\(x^2 - 2x + 1 = 0\)**: This can be factored as \((x - 1)(x - 1) = 0\). This is also a perfect square.

3. **\(2x^2 + 14x + 12 = 0\)**: To factor this, we can first factor out a 2:
\(2(x^2 + 7x + 6) = 0\), which can then be factored as \(2(x + 6)(x + 1) = 0\).

4. **\(2x^2 - 2x - 10 = 0\)**: We can factor out a 2 first:
\(2(x^2 - x - 5) = 0\). The quadratic \(x^2 - x - 5\) does not factor neatly using integers, and the standard method of grouping doesn't apply here directly.

From this analysis, the fourth equation \(2x^2 - 2x - 10 = 0\) is not solvable by grouping because it does not factor nicely with integer values.

Therefore, **the answer is:** \(2x^2 - 2x - 10 = 0\).