Factor:

-3x^2 - 18x + 15

-3x^2 - 18x + 15

since 3x^2 + 18x - 15 = 0 does not have any rational roots since b^2 - 4ac is not a perfect square,
it does not factor over the rationals

To factor the quadratic expression -3x^2 - 18x + 15, we need to determine two binomials such that when multiplied together, they produce the original quadratic expression.

The first step is to look for any common factors among the three terms. In this case, we see that all three terms have a common factor of -3. By factoring -3 out, we get:

-3(x^2 + 6x - 5)

Now, we focus on factoring the quadratic expression within the parenthesis, x^2 + 6x - 5.

To factor this quadratic trinomial, we need to find two binomials in the form (x + a)(x + b) that multiply to give x^2 + 6x - 5.

To find the values of a and b, we need to determine two numbers whose product is -5, and whose sum is 6. In this case, the numbers that satisfy these conditions are 5 and -1.

Therefore, we can write x^2 + 6x - 5 as:

(x + 5)(x - 1)

Putting it all together, we have factored -3x^2 - 18x + 15 as:

-3(x + 5)(x - 1)