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 different factors for −7x
in Step 1.
Use different factors for negative 7 x in Step 1.

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

Answer 1

To arrive at a shared binomial in Step 3, Kevin should consider how he factored the terms in Step 2. In Step 3, he ended up with \(3x(2x-1) + 2(-2x+1) = 0\), which shows that he factored the terms in such a way that they do not share a common binomial factor.

The appropriate change Kevin should make is to change the grouping of pairs in Step 2. This would allow him to group the terms in a way that may yield a common binomial factor when he factors them in Step 3.

Therefore, the correct response is:

Change the grouping of pairs in Step 2.