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#QUADRATIC BINOMIAL HOW TO#
We’ll take a closer look at each case, a shortcut formula, and some examples so you will know exactly how to solve them. Also remember that quadratic binomials with b = 0 are even functions. Note that in the second case, we might also need to factor out a GCF (greatest common factor) first in order to factor completely and to make our work easier. However, we might need to use complex numbers for some quadratic binomials in this case (we can check the discriminant to find out when this is the case!) Case 2: b = 0 – this case can be factored as a difference of squares.No complex numbers will be necessary here: one root is zero, and the other is –b/a. Case 1: c = 0 – this case is fairly easy to factor, since both nonzero terms have an x that we can factor out.There are two basic cases to consider when factoring a quadratic binomial of the form ax 2 + bx + c = 0: Let’s take a closer look at each of these. This is what gives us our two cases for factoring a quadratic binomial: whether we have b = 0 (zero linear term) or c = 0 (zero constant term). It must always have an x 2 term (since a cannot equal zero in a quadratic) and one other term: either an x term (linear) or a constant term that has a nonzero coefficient. Putting these definitions together, a quadratic binomial is a quadratic with two terms. 2x 2 – 13x (the constant term is zero here)Īlso, remember that a binomial has two terms added together (sort of like how a bicycle has two wheels).
![quadratic binomial quadratic binomial](https://i.ytimg.com/vi/Pc-DljBq3Q8/maxresdefault.jpg)
![quadratic binomial quadratic binomial](https://i.ytimg.com/vi/3mQlEwsMJGI/maxresdefault.jpg)
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How To Factor A Quadratic Binomialįactoring a quadratic binomial is more straightforward than factoring a quadratic trinomial. We’ll also talk about the shortcut formulas and where they come from. In this article, we’ll talk about how to factor a quadratic binomial and look at several examples of each of the two cases. Of course, you can also derive these shortcut formulas from the quadratic formula by plugging in either b = 0 or c = 0 as the case may be. When the linear term is zero (b = 0), the quadratic binomial factors as a(x + r)(x – r) with roots r and –r, where r is the square root of -c/a. So, how do you factor a quadratic binomial? For a quadratic binomial in standard form, if the constant term is zero (c = 0), the quadratic binomial factors as x(ax + b) with roots x = 0 and x = –b/a. You might be hoping for some shortcuts for factoring quadratic binomials – luckily, there are some that you can use! Quadratic equations come up all the time in algebra, as do binomials.