Final answer:
The quadratic polynomial 9x²-39x-30 can be factored completely by finding two numbers that multiply to -270 and add up to -39, which are -45 and 6. This leads to the factors (3x + 2)(3x - 15).
Step-by-step explanation:
The student's question involves factoring a quadratic polynomial completely. The given polynomial is 9x²-39x-30. To factor this, we first look for two numbers that multiply to give the product of the coefficient of x² term (which is 9) and the constant term (which is -30), and add up to the coefficient of the x term (which is -39).
After some trial and error, we can find that -45 and 6 are the two numbers that satisfy these conditions (-45 * 6 = -270, and -45 + 6 = -39). We can then rewrite the middle term of the quadratic and factor by grouping:
9x² - 45x + 6x - 30 = 3x(3x - 15) + 2(3x - 15) = (3x + 2)(3x - 15)
Thus, the polynomial 9x²-39x-30 is factored completely as (3x + 2)(3x - 15).