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

Question

Responses

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

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

x^2−12x+35=0
x squared minus 12 x plus 35 equals 0

2x^2+14x+12=0

Answer 1

To determine which of the given quadratic equations is not solvable by grouping, we can check if they can be factored easily into binomials.

1. 2x² - 2x - 10 = 0

   • First, factor out the common factor of 2: \[ 2(x² - x - 5) = 0 \]
   • The quadratic \( x² - x - 5 \) does not factor nicely into integers.

2. x² - 2x + 1 = 0

   • This can be factored as: \[ (x - 1)(x - 1) = 0 \]
   • It has a double root and is easily factored.

3. x² - 12x + 35 = 0

   • This can be factored as: \[ (x - 5)(x - 7) = 0 \]
   • It factors nicely into integers.

4. 2x² + 14x + 12 = 0

   • We can factor out 2: \[ 2(x² + 7x + 6) = 0 \]
   • The quadratic \( x² + 7x + 6 \) can be factored as: \[ (x + 1)(x + 6) = 0 \]

From the analysis, the quadratic equation that is not easily factored into integers (and thus not solvable by grouping) is:

2x² - 2x - 10 = 0.