Which of the following quadratic equations is not solvable by factoring?(1 point) Responses 2x2+14x+12=0 2 x squared plus 14 x plus 12 is equal to 0 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 2x2−2x−10=0

Answer 1

To determine which of the given quadratic equations is not solvable by factoring, we can check the discriminants of each one or attempt to factor them directly.

1. 2x² + 14x + 12 = 0

   We can factor out a 2: \( 2(x² + 7x + 6) = 0 \)

   Now, factor the quadratic: \( x² + 7x + 6 = (x + 1)(x + 6) \)

   Thus, it is factorable.

2. x² - 12x + 35 = 0

   This factors directly as: \( (x - 5)(x - 7) = 0 \)

   So, it is factorable.

3. x² - 2x + 1 = 0

   This factors to: \( (x - 1)(x - 1) = (x - 1)² = 0 \)

   Thus, it is also factorable.

4. 2x² - 2x - 10 = 0

   We can first factor out a 2: \( 2(x² - x - 5) = 0 \)

   Now we check if \( x² - x - 5 \) can be factored. The discriminant (\(b² - 4ac\)) is: \[ (-1)² - 4(1)(-5) = 1 + 20 = 21 \] The discriminant is positive, but since it does not yield a perfect square, it is not factorable over the integers.

Therefore, the equation that is not solvable by factoring is 2x² - 2x - 10 = 0.