Question

Kevin is solving 6x2−7x+2=0
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.

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

Change the grouping of pairs in Step 2.

Answer 1

To help Kevin arrive at a shared binomial in Step 3, he should consider using a different approach to factor the expression in Step 1. The issue lies in the way he grouped and factored the terms.

One effective change would be to **use different factors for -7x in Step 1**. Instead of grouping as he currently did with \(-3x\) and \(-4x\), he could instead use \(-6x\) and \(-x\) because:

\[
-6x + (-x) = -7x
\]

This would lead Kevin to rewrite the equation in a way that makes it possible to group and factor out the shared binomial.

So, the correct response would be:

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