In Exercises 49–56, factor each perfect square trinomial. x^2−14x...

Question

In Exercises 49–56, factor each perfect square trinomial. x^2−14x+49

Accepted Answer

Hello. Today we're going to be factoring a given try no meal. So the tri no meal given to us is X squared minus 18 X plus 81. Now when we factor this trin Amiel, our end result is going to be a product of two mono meals that involved the factors for the first term and the last term. Well if you notice our first term in last term are perfect squares. The first term can be rewritten as X squared and the last term 81 could be rewritten as nine squared. So that means that when we factor this binomial, we're going to get to mono meals that involve the terms X at nine but we need to decide whether these are gonna be differences or sums while if we look at the signs of our given tryin Amiel the signs are minus and plus. So that means that both of these mono me als are going to be differences. Now we need to verify if this is the correct factory ization. And in order to verify that we can go ahead and foil these mono meals together and this should give us our original try no meal. So when we factor this together, X times X is going to give us X squared x times negative nine is going to give us negative nine X negative nine times X is going to give us negative nine X and negative nine times negative nine is going to give us positive 81 combining the like terms together which are both of the negative nine X. We're going to get the trine. Amiel X squared minus 18 X plus 81. And this verifies that this is the correct Factory Ization for a given try no meal. Okay, so now, if you notice our Factory Ization is the product of two of the same quantities X minus nine, so we can go ahead and combine this together to a single quantity and rewrite it as X minus nine squared. And this is going to be the Factory ization of our given try no meal. And the answer to this problem is going to be D. So I hope this video helps you in understanding how to factor this type of try no meal and I'll go ahead and see you all in the next video.

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