Kevin is solving 6x2−7x+2=0

Question

by grouping. He performed the first three steps as shown below. However, he struggles to complete Step 4 because he could not come up with a shared binomial in Step 3. What change should Kevin make to arrive at a shared binomial in Step 3?

Step 1: 6x2+(−3x)+(−4x)+2=0

Step 2: (6x2+(−3x))+(−4x+2)=0

Step 3: 3x(2x−1)+2(−2x+1)=0

(1 point)
Responses

Use −2
as the GCF of the second grouping in Step 3.
Use negative 2 as the GCF of the second grouping in Step 3.

Change the grouping of pairs in Step 2.
Change the grouping of pairs in Step 2.

Use −3x
as the GCF of the first grouping in Step 3.
Use negative 3 x as the GCF of the first grouping in Step 3.

Use different factors for −7x
in Step 1.

Answer 1

To arrive at a shared binomial in Step 3, Kevin should change the grouping of pairs in Step 2.

In his initial setup, he grouped \(6x^2 + (-3x)\) and \((-4x + 2)\). Instead, if he regrouped the terms to pair \(6x^2\) with \(-4x\) and \((-3x + 2)\), he would be more likely to find a common factor that enables him to achieve a shared binomial in the next step. This change would lead to factoring methods that yield a common binomial factor, helping him proceed with the solution.

Therefore, the correct answer is:

Change the grouping of pairs in Step 2.