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

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

2x2−2x−10=0

Answer 1

To determine which of the given quadratic equations is not solvable by grouping, we'll analyze each equation.

1. \(x^2 - 12x + 35 = 0\):

   • Factors: \( (x - 5)(x - 7) = 0 \)
   • This can be solved by finding the roots.

2. \(x^2 - 2x + 1 = 0\):

   • Factors: \( (x - 1)(x - 1) = 0 \) or \( (x - 1)^2 = 0 \)
   • This can also be solved by finding the roots (perfect square).

3. \(2x^2 + 14x + 12 = 0\):

   • We can factor out a 2: \( 2(x^2 + 7x + 6) = 0 \)
   • Then, it factors as \( 2(x + 1)(x + 6) = 0 \)
   • This can be solved by finding the roots.

4. \(2x^2 - 2x - 10 = 0\):

   • First, divide the entire equation by 2: \( x^2 - x - 5 = 0 \)
   • This quadratic does not factor nicely and does not lend itself to grouping.

Among the given options, the equation \(2x^2 - 2x - 10 = 0\) (or simplified \(x^2 - x - 5 = 0\)) is the one not easily solvable by grouping, as its factors are not integers.

So, the answer is \(2x^2 - 2x - 10 = 0\).