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 different factors for −7x
in Step 1.
Use different factors for negative 7 x in Step 1.
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 −2
as the GCF of the second grouping in Step 3.
1 answer
To arrive at a shared binomial in Step 3, Kevin should change the grouping of pairs in Step 2.
Currently, in Step 2, he groups \( (6x^2 + (-3x)) \) and \( ((-4x) + 2) \). If he changes the grouping to \( (6x^2 + 2) + ((-3x) + (-4x)) \), it will allow for a common binomial factor to emerge in the next step.
Therefore, the correct response is:
Change the grouping of pairs in Step 2.
