Which Binomial Is A Factor Of 9X2 64?

Introduction

In algebra, a binomial is an expression consisting of two terms that are separated by either a plus or minus sign. A factor, on the other hand, is a term that divides another term without leaving a remainder. In this article, we will discuss which binomial is a factor of 9x2 64.

Factorization of 9x2 64

To find out which binomial is a factor of 9x2 64, we need to factorize it first. Factoring is the process of breaking down an expression into its smaller components. In this case, we can factorize 9x2 64 using the difference of squares formula, which states that: a2 - b2 = (a + b) (a - b) In our case, a is 3x and b is 8. Therefore, we can write: 9x2 64 = (3x + 8) (3x - 8)

Binomial as a Factor

Now that we have factored 9x2 64, we can easily see that both (3x + 8) and (3x - 8) are factors of 9x2 64. This means that either of these binomials can divide 9x2 64 without leaving a remainder. To understand this better, let's take an example. If we divide 9x2 64 by (3x + 8), we get: 9x2 64 ÷ (3x + 8) = 3x - 8 As we can see, (3x + 8) divides 9x2 64 without leaving a remainder, and the result is (3x - 8). Similarly, if we divide 9x2 64 by (3x - 8), we get: 9x2 64 ÷ (3x - 8) = 3x + 8 Once again, we see that (3x - 8) is a factor of 9x2 64, and dividing by it gives us (3x + 8) as the result.

Conclusion

In conclusion, we can say that both (3x + 8) and (3x - 8) are factors of 9x2 64. We arrived at this conclusion by factorizing 9x2 64 using the difference of squares formula. This means that either of these binomials can divide 9x2 64 without leaving a remainder. It is important to note that there may be other binomials that can also be factors of 9x2 64, but for this particular expression, (3x + 8) and (3x - 8) are the only two binomials that are factors.