Factor each polynomial. See Example 7. a^4-2a^2-48

Question

Accepted Answer

Hey everyone here we are asked to factor the following polynomial of B to the fourth power minus three, B squared minus 28. Now, taking a look at our expression here we see that the highest power is four. But we are used to factoring expressions where the highest power is too. So we I want to start by simplifying our expression and we can do this by letting the variable U be equal to B squared. So now we just need to rewrite our given expression using this variable U. So doing this. We have U squared minus three, you minus 28. And so now we see that we have a much simpler expression to work with so we can begin factoring and we need to consider the factor as the quantity of a. U. Plus B times the quantity of C. U plus D. And so now we need to find the value of A. C. And we also need to find the value of B. D. And then we need to find the factors. So starting with our value for A C. Well this is just going to be the coefficient of our first term which is just one. So A C is just one. And now for B. D. Well B D. Is just the value of our third term here which is negative 28. And so now we need to find the factors of both of these values. Starting with a C. Which is just one of the factors of one are just one and one or negative one and negative one. And then for B D We have negative 28 which has the factors of negative 28 28 and negative 1 14 and negative two negative 14 and positive two or four and negative seven or negative four and positive seven. So now with all of the factors identified, we just have to go through a trial and air process to find a factored form that returns our simplified expression from earlier. So after going through this trial and error process, we see that our factored form for the simplified expression of U squared minus three U minus 28 turns out to be you plus four. The quantity of U plus four times the quantity of U minus seven. And so now the last appears to just substitute in this value for you from which we had from earlier. So we just had to substitute back in B squared which gives us our final factored answer of the quantity of B squared plus four times the quantity of B squared minus seven. And with this we have found our fully factored form of our original expression and therefore we are left with answer choice. C Thanks for watching. I hope you found this video helpful and I'll see you again next time

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Factor each polynomial. See Example 7. a^4-2a^2-48

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