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 modify how he groups the terms in Step 2. The ideal approach is to use different factors for -7x in Step 1.

Step 1 should be adjusted to use factors that align well for grouping. For instance, instead of -3x and -4x, if he uses -2x and -5x, he can set up the grouping in such a way that both parts will yield a common factor.

So, the correct change is:

Use different factors for −7x in Step 1.

This way, when he completes the grouping, he will be able to create a shared binomial in Step 3.