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

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.
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 help Kevin arrive at a shared binomial in Step 3, he should use different factors for −7x in Step 1.

Currently, Kevin correctly breaks down \(-7x\) into \(-3x\) and \(-4x\), but he can use other factors, such as \(-2x\) and \(-5x\), which would lead to a shared binomial in Step 3.

Here's how that looks:

Step 1: 6x² + (−2x) + (−5x) + 2 = 0

Step 2: (6x² + (−2x)) + ((−5x) + 2) = 0

Step 3: 2x(3x − 1) + (−1)(5 − 2) = 0

Thus, changing the factors used in Step 1 allows for grouping that reveals a common binomial in the next steps.