Question

5. 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 is equal to 0

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

Answer 1

To determine which of the given quadratic equations is not solvable by grouping, we first need to understand what grouping entails. In general, grouping is a method used to factor a polynomial by grouping the terms into pairs or groups that can be factored out.

Let's analyze each of the quadratic equations provided:

1. **\(2x^2 + 14x + 12 = 0\)**

This can be factored by grouping. First, factor out the GCF (2):
\[
2(x^2 + 7x + 6) = 0
\]
Then, we can factor the quadratic inside the parentheses:
\[
x^2 + 7x + 6 = (x + 6)(x + 1)
\]

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

This equation can also be factored. It factors directly:
\[
(x - 5)(x - 7) = 0
\]
Grouping is not necessary here, but it can still be considered solvable.

3. **\(2x^2 - 2x - 10 = 0\)**

First, divide the entire equation by 2:
\[
x^2 - x - 5 = 0
\]
This does not factor neatly, and thus cannot be solved by grouping.

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

This can be factored straightforwardly:
\[
(x - 1)(x - 1) = 0
\]

From the analysis, the equation **\(2x^2 - 2x - 10 = 0\)** is the one that does not factor neatly. Therefore, it cannot be solved by grouping as effectively as the others.

**Answer:** \(2x^2 - 2x - 10 = 0\) is not solvable by grouping.