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 −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.

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

Answer 1

To arrive at a shared binomial in Step 3, Kevin should consider how he factored the expressions in the first and second groupings. In the solution process he followed, the factors he chose provided different binomials, which is why he struggled to find a shared binomial.

The correct response is:

Use different factors for −7x in Step 1.

Instead of using \(-3x\) and \(-4x\), he can rewrite \(-7x\) as, for example, \(-2x - 5x\), which would give him a consistent binomial common across the grouping. This would lead to a shared binomial being factored out in Step 3, allowing him to complete the problem correctly.