In Exercises 17–38, factor each trinomial, or state that the trin...

Question

In Exercises 17–38, factor each trinomial, or state that the trinomial is prime. 3x^2+4xy+y^2

Accepted Answer

Hello. Today we're going to be factoring a polynomial. So the polynomial given to us is four X squared plus five X, Y plus y squared. Now, in its current form, this polynomial is not factory ble however, we can rewrite it into a factory ble form because our middle term five X Y could be rewritten as the sum of four X Y plus x, Y. So if we rewrite our middle term as this, some are polynomial turns into four X squared plus four X, Y plus X, Y plus Y squared. And now that we have a polynomial of four terms, we can go ahead and factor by using factoring by grouping. So factoring by grouping allows us to group up our first two terms and our last two terms together. And we're gonna go ahead and identify the greatest common factor between the two groups. For our first group are two terms are four X squared and four X. Y. Both of these terms have a common factor of four X. So this first group has the greatest common factor of four X. And for the right hand group we have X, Y plus y squared. Both of these terms have the common term Y. So this has the greatest common factor of why? So if we go through and factor out our greatest common factors, the first group is gonna turn into four X times the quantity X plus Y. And if we factor out why from our right hand group, what that gives us is positive Y times X plus Y. Now both of these terms here have the common term X plus Y. So we can combine both of these quantities into a single quantity. And in order to do that, we just want to go ahead and add the leading coefficients together and combine both of the ex wives together. Doing so is going to give us the quantity four X plus Y, times X plus Y. And this is going to be the fully factored version of our given polynomial. And that means that the answer to this problem is going to be be so. I hope this video helps you in understanding how to factor this type of polynomial. And I'll go ahead and see you all in the next video.

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