The area of a rectangular painting is given by the trinomial x^2+2x-15. What are the possible dimensions of the painting? Use factoring.

(x-3)(x+5) = ?

(x-3)(x+5)

well, if x were 4 It could be 9 x 1
or if x were 5 it could be 10 x 2
or if x were 6 it could be 11 x 3
or if x were 7 it could be 12 x 4
etc

To find the possible dimensions of the painting, we need to factor the given trinomial. The factored form of the trinomial x^2 + 2x - 15 can be determined by looking for two numbers whose product is equal to -15 and whose sum is equal to 2.

Let's list all possible factor pairs of -15:
1, -15
-1, 15
3, -5
-3, 5

From these factor pairs, we can see that the factors whose sum is equal to 2 are -3 and 5. Therefore, the factored form of the trinomial x^2 + 2x - 15 is (x - 3)(x + 5).

Now, let's consider the possible dimensions of the painting. The factored form (x - 3)(x + 5) tells us that one dimension must be (x - 3) and the other dimension must be (x + 5). So, the possible dimensions of the painting are (x - 3) and (x + 5).

In summary, the possible dimensions of the painting, using factoring, are (x - 3) and (x + 5).