Question

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

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

2x2−2x−10=0
2 x squared minus 2 x minus 10 equals 0

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

x2−2x+1=0

Answer 1

To determine which quadratic equation is not solvable by grouping, we will look at the given equations and see if they can be factored by grouping.

1. **\(2x^2 + 14x + 12 = 0\)**
This can be factored. The expression can be rewritten as \(2(x^2 + 7x + 6)\), which factors further to \(2(x + 6)(x + 1)\).

2. **\(2x^2 - 2x - 10 = 0\)**
This can also be factored. First, divide the equation by 2: \(x^2 - x - 5 = 0\). This does not factor easily into integers but can be solved using the quadratic formula. Grouping may not be straightforward here, depending on how you view it.

3. **\(x^2 - 12x + 35 = 0\)**
This factors as \((x - 5)(x - 7) = 0\).

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

Among these, the second equation \(2x^2 - 2x - 10 = 0\) is the least suitable for grouping as it doesn't easily lend itself to a simple factorization method. Therefore, this is the equation that is not solvable by grouping.

**Final Answer: 2x² - 2x - 10 = 0**