Determine if x2 + 18x + 81 is a perfect square trinomial and factor. a. (x+9)^2 b. (x-9)^2 c. (x+81)^2 d. not a perfect square trinomial.

The answer is A. (X+9)^2

Hey there!

Before we start, be sure to remember that when factoring, you need to remember your factors need to add to the middle term and multiply to the final term. Let's go through out options.

Using foil, let's evaluate A-

(x+9)(x+9) = x^2 + 9x + 9x + 81 = x^2 + 18x + 81

Therefore, A is our answer. Let's look at why the others don't work.

B) (x-9)(x-9) = x^2 - 9x - 9x + 81 = x^2 -18x + 81

It doesn't work because the middle term isn't supposed to be negative.

For C, we don't have to evaluate because out of estimation, we realize the number 81 as a factor is too large to be able to use to factor for a number like 18.

Finally, we can't say it's not a perfect square trinomial because by factoring and testing it, we've just proved that it is.

Hope this helps!