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

Question

Responses

x2−12x+35=0
x squared minus 12 x plus 35 is equal to 0

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

Answer 1

To determine which of the given quadratic equations is not solvable by grouping, we need to look for equations that cannot be factored simply as the product of two binomials.

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

2. \(2x^2 - 2x - 10 = 0\): We can factor out a 2 first:
   \(2(x^2 - x - 5) = 0\)
   The quadratic \(x^2 - x - 5\) doesn't factor nicely, but would generally require the quadratic formula.

3. \(x^2 - 2x + 1 = 0\): This can be factored as \((x - 1)(x - 1) = (x - 1)^2 = 0\).

4. \(2x^2 + 14x + 12 = 0\): We can factor out a 2 first:
   \(2(x^2 + 7x + 6) = 0\)
   The quadratic \(x^2 + 7x + 6\) can be factored as \((x + 1)(x + 6) = 0\).

The equation that is not easily factorizable by grouping or does not yield integers when set up for factoring is \(2x^2 - 2x - 10 = 0\) because after factoring out the 2, the remaining quadratic does not have integer solutions.

Thus, the answer is:

2x² - 2x - 10 = 0 is not solvable by grouping.