How to Write a Polynomial in Factored Form

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Writing a polynomial in factored form is something that you can do as X = 2X squared - 12X + 22. Write a polynomial in factored form with help from an experienced mathematics educator in this free video clip.

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Video Transcript

Hello, my name is Walter Unglaub. And this is how to write a polynomial in factored form. So, if we're given a polynomial, in this case, a quadratic polynomial. We have F of X is equal to two-X squared minus 12-X plus 22. The first step in terms of factoring a polynomial, is to find a common factor that exists in all of the terms. In this case, we can easily identify that common factor as two. Since two goes evenly into itself, 12 and 22. So, what we do is we multiply our function, our polynomial by one. But one here is in terms of two divided by two. And on the left hand side, that simply becomes F of X times one. And on the right hand side, I leave the two in the numerator, untouched and I divide the coefficients of each of the terms in the polynomial by this denominator. So, I have two-X squared divided two minus 12-x divided two, plus 22 divided two. This simplifies because this first term, you just get one in the coefficient. For the second term, you get a six and finally, for this constant right here, you get 11. So, we have two times X squared minus six-X plus 11. The next step is to complete the square. Since this is a quadratic relationship, we can identify the form X minus A squared plus B. And we want to rewrite this portion of our worked out example. So, to get A, what we do is, we take the coefficient of the linear term and we divide it by two. So, we have negative six divided two, which gives us negative three. So, we see that A is going to be equal to three in this case. So, we have F of X is equal to two times X minus three squared plus a constant B. In order to determine this constant B, we need to subtract from this constant, the square of this number. So, if we square negative three, we get nine. And so 11 minus nine is equal to two. And this is our B. So, finally we have a factored form for the original polynomial and it's written. Which is the common factor for all terms in the original expression, times X minus three squared plus two. Which could be rewritten as two-X minus three squared plus four. My name is Walter Unglaub. And this is how to write a polynomial in a factored form.


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