In Exercises 49–56, factor each perfect square trinomial. 4x^2...

Question

In Exercises 49–56, factor each perfect square trinomial. 4x^2+4x+1

Accepted Answer

Hello today we're going to be factoring a given try no meal. So the tri, no meal given to us is nine X squared plus X plus four. Now when we factor this, try no meal, our end result is going to be a product of two mono meals that involve the factors of our first term and our last term. Now if we pay attention to the first term in last term, both of them are perfect squares nine X squared can be rewritten as three X to the power of two and four can be rewritten as two squared. So when we factor this try no meal, we're gonna get to mono meals that have both the terms three X and two inside of them. Now the only thing we need to decide is are these going to be positive or negative quantities? Well if we take a look at our original try no meal, all of the terms here are positive. So both of our mono meals here are going to have to be sums now in order to verify if this is the correct Factory ization, we can go ahead and foil these quantities together to show that we get our original try no meal. So if we foil these quantities together three x times three X is going to give us nine x squared three x times two is going to give us six x two times three X is going to give us six x and two times two is going to give us four combining the like terms which are both of the positive, six x is going to give us nine X squared plus X plus four and this verifies that this is the factor to our original try no meal. Now, if you notice our factor are two mono meals that are the exact same quantity three X plus two and three X plus two. So we can go ahead and combine this into a single quantity which can be written as three X plus two squared. And this is going to be the factored version of our given Trina meal. And the answer to this problem is going to be a 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.

In Exercises 49–56, factor each perfect square trinomial. 4x^2+4x+1

Key Concepts

Perfect Square Trinomial

Factoring

Quadratic Expressions

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