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.

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.