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

Question

In Exercises 49–56, factor each perfect square trinomial. x^2+2x+1

Accepted Answer

Hello today we're gonna be factoring a given try no meal. So the tri no meal given to us is X squared plus eight X plus 16. Now when we factor this tryin Amiel we're going to end up with the product of two Mon Ami Als and both of these Minami als are gonna involve the factors of our first term and last term. Now if you notice the first term and last term of our given try no meals are perfect squares, X squared can be rewritten as X raised to the power of two and 16 can be rewritten as four squared. So when we factor this trin Amiel, both of the mono meals are gonna involve factors of X and four. Now we need to go ahead and decide whether these are going to be sums or differences. Well if we look back to our original try no meal, all of the terms inside of our try no meal are positive. That means that both of these mono meals are going to need to be sums Now we need to verify that this is the correct factory ization to our try no meal and in order to verify that we can just go ahead and foil them together and doing so should give us the original try no meal. So when we factor these two quantities together, X times X is going to give me X squared X times four is going to give me positive four x four times X is going to give me positive four x and four times four is going to give me 16 when we combine the like terms together, which are both of the positive for excess. That's going to give us X squared plus eight X plus 16. And this verifies that. This is the correct Factory Ization to our original try no meal. Okay, now, if you notice our Factory Ization involves two quantities that are exactly the same X plus four times X plus four. So we can go ahead and condense this together as a single quantity and write it as X plus four squared. And this is going to be the Complete Factory Ization to our original Try no meal. And the answer to this problem is going to be B So I hope this video helps you in understanding how to factor this binomial and I'll go ahead and see you all in the next video.

In Exercises 49–56, factor each perfect square trinomial. x^2+2x+1

Key Concepts

Perfect Square Trinomial

Factoring

Binomial

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