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

Question

Factor out the greatest common factor from each polynomial. See Example 1. 5h^2j+hj

Accepted Answer

Welcome back. I am so glad you're here. We are given this expression S. T minus 21 S squared T. And we are asked to factor it, will we recall from previous lessons that we are going to take a look at these two terms here being subtracted from one another. And we are going to compare them asking ourselves do they share any common factors that we can factor out in front? And more specifically, we're going to compare the parts that are similar to each other. So the whole numbers that that unwritten one in front of the S. T. The S. And S. Squared and the T. And the T. And ask ourselves do they share anything that we can factor out? So let's take a look first at the one and the negative 21. No, we can't really factor anything out of that. The greatest common factor is one. We can't really factor out a one. So nothing gets factored out of the whole numbers. Let's take a look at the S. And the S. Squared. Well when we have variables with exponents, we're going to look at their degrees. The degree here of two. And this one's an unwritten degree of one. We're going to find the variable with the lowest degree which in this case is one. So that's s to the first and we're going to divide both of them by the variable with the lowest degree. So we'll divide both of them by s meaning that we can factor out and s Alright, now let's compare our T. S. We have T and T. Well both T. And T. Are divisible by T. So we can pull out a factor of T. Now what's left. Well now is where we do that division that we set up on the right hand side and with the one from the first one. Um That is just a one that will still be there. This S to the first divided by S. That also equals one. So we've got a one times a one for whole numbers in R. S. And T divided by T. Is also one. So we've got one times one times one and that equals one. We need to be sure we include that one there. All right now let's do the second part. This negative 21 needs to come down for our whole numbers this s square divided by S. S. Square divided by us. We're going to take the variable exponents and subtract them when we are dividing and two minus one is one. So that leaves just S on the inside and now T divided by T. Again that is one. And because we have that negative 21 S there we don't need to put a one because negative 21 S. Times one is negative 21 S. And that's what we've got. All right now this has been as factored as it can be. We look at our answer choices and this matches with answer choice C. Well done. We'll catch you on the next one

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Factor out the greatest common factor from each polynomial. See Example 1. 5h^2j+hj

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