In Exercises 45–68, factor by grouping.

10x² − 12xy + 35xy − 42y...

Question

In Exercises 45–68, factor by grouping.

10x² − 12xy + 35xy − 42y²

Accepted Answer

Hello, today we're going to be factoring the given polynomial. So what we are given is a polynomial of four terms. And whenever we see a polynomial of four terms, that is an indication that we should try factoring by grouping. Now, factoring by grouping allows us to group up the first two terms of the polynomial and the last two terms of the polynomial together. And what we want to go ahead and do is factor out a common factor from both of the groups. So taking a look at the first group, we have 12 M squared minus 15 M N looking at the coefficients 12 and 15. Both of these are multiples of three. So we can go ahead and factor out a three from the first group and we have M squared and M N in both of the terms, there is at least one instance of em in both of the terms. So we can go ahead and factor out an M from the first group. So in total, we're going to be factory now three M from the first group and factory. Now a three M allows us to rewrite the group as three M times the quantity four M minus five N. And now we want to go ahead and repeat this process for the second group. In the second group, we have 32 MN minus 40 N squared, 32 and 40 are both multiples of eight. So we can go ahead and factor out an eight from 32 and 40. And we have M N and N squared, there's at least one instance of N in both of the terms. So we can also factor out an N from the second group. So factory, now A N from the second group is going to allow us to rewrite it as positive eight N times the quantity four M minus five N. Now notice that after we factored out a common factor, we have two instances of the group four M minus five N, we can go ahead and combine these into a single group of four M minus five N by combining the coefficients together and combining the coefficients together is going to allow us to rewrite this as three M plus eight N times the quantity four M minus five N. And this is going to be the factored version of the given polynomial. And with that being said, the answer to this problem is going to be a. So I hope this video helps you in understanding how to approach this problem. And I'll go ahead and see you all in the next video.

In Exercises 45–68, factor by grouping. 10x² − 12xy + 35xy − 42y²

Key Concepts

Factoring by Grouping

Common Factors

Binomial Factors

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