In Exercises 93–100, factor completely.x² − 6/25 + 1/5 x

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Accepted Answer

Hello, today we're gonna be factoring the following tri trinomial completely. So what we are given is X squared minus 15/49 plus 2/7 X. Now, before we factor this, let's quickly reorder the terms going from highest exponent to least exponent. And that can be reordered as X squared plus 2/7 X minus 15/49. So what we have is a trinomial with the leading coefficient of one. So what we want to go ahead and do is list out the factors of the last term and the factors of the last term should multiply together to give us the last term. But add up to give us 2/7 X and two possible factors for negative 15/49 can be negative 3/7 and 5/7 or it could be positive 3/7 times 5/7. And the factors of the first term are just going to be X and X. So let's go ahead and test out negative 3/7 and 5/7. If we put this into the factored form of a trinomial, what we get is X minus 3/7 times X plus 5/7. And now, in order to verify that this is the correct factored form, we need to go ahead and foil the quantities together by foiling the quantities together. We multiply X with X which is going to give us X squared, we multiply X with 5/7, which is going to give us positive 5/7 X, we multiply negative 3/7 with X, which is going to give us negative 3/7 X. And finally, we multiply negative 3/7 with 5/7, which is going to give us negative 15/49. We can go ahead and combine the light terms which is 5/7 X and negative 3/7 X. And that is going to give us X squared plus 2/7 X minus 15/49. And this matches the original trinomial, which means that X minus 3/7 times X plus 5/7 is going to be the complete factorization of the original trinomial. And with that being said, the answer to this problem is going to be B so I hope this video helps you in understanding how to approach this problem. And I'll go ahead and see you all in the next video.

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In Exercises 93–100, factor completely.x² − 6/25 + 1/5 x

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