Factor out the greatest common factor from each polynomial. See E...

Question

Factor out the greatest common factor from each polynomial. See Example 1. xy-5xy^2

Accepted Answer

Welcome back. I am so glad you're here. We are given this expression 17 M. N squared plus M. N. And we are asked to factor this. We recall from previous lessons that we are going to take a look at these two terms being added here and we are going to compare them. We're going to look at them and say, Are there any factors that are shared? Are there any things being multiplied that we can pull out that they have in common? And more specifically, we will compare the things that are similar. So we can look at the whole numbers, the 17 and the first one and an unwritten one here. In the second one we've got an M. And an M. And we've got an N. Squared and an N. So we can compare these and see what factors they share that. We can factor out. So the first ones, we've got our whole numbers are 17 and a one and the greatest common factor between 17 and one is one. And we can't really factor out on one. So there's nothing to factor out there. Now we've got an M. And an M. While M. And M are both divisible by M. They have a factor of M. So we can factor out an M. Now we've got N. Squared and N. Well when we've got variables with degrees, we're going to compare their degrees. We've got a two for the first one and an unwritten one for the second one and we're going to look for the variable with the lowest degree. They are both divisible by the variable with the lowest degree. So in this case they're both divisible by end to the first or end. And that end is exactly what we will factor out. So we factored out an M. N. Now what's left on the inside? Well, for the whole numbers we didn't factor anything else, so we can bring down that 17. Now we can do the division on the right hand side. We've got M divided by M. That leaves us with one. So we've got 17 times one which is 17. So we don't need to put that one down there. Now we've got N squared divided by N. Well when we've got two variables being divided, we are going to subtract their exponents. So two minus one equals one. So this equals end to the first or N. So we can write our N. That's left over here inside the parentheses. Alright, now, for the second one we've got that one that we're bringing down and now we've got M divided by M. For M. S. That also equals one. So we've got one times one so far and end the first divided by N also equals one. So we've got one times one times one. We need to be sure that we put in a plus one for that one times one. Times one. We factored everything out of the second part. All right. So this is as factored as it's going to get M. N. Times 17. N. plus one. We look at our answer choices and this matches with answer choice. D. Well done. We'll catch you on the next one.

Factor out the greatest common factor from each polynomial. See Example 1. xy-5xy^2

Key Concepts

Greatest Common Factor (GCF)

Factoring Polynomials

Polynomial Terms

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