How do you factor #8y^2 + 17y + 9#?

Discriminant: D = b^2 - 4ac = 289 - 288 = 1. Since D is not a perfect square, the function can't be factored.

To factor the quadratic expression (8y^2 + 17y + 9), you can use the factoring by grouping method or the quadratic formula. Let's use the factoring by grouping method:

1. Multiply the leading coefficient (8) by the constant term (9): (8 \times 9 = 72).
2. Find two numbers that multiply to 72 and add to the coefficient of the middle term (17). The numbers are 8 and 9.
3. Rewrite the middle term (17y) using the two numbers found in the previous step: (17y = 8y + 9y).
4. Group the terms: (8y^2 + 8y + 9y + 9).
5. Factor by grouping: ((8y^2 + 8y) + (9y + 9)). (8y(y + 1) + 9(y + 1)).
6. Notice that (y + 1) is common to both terms. Factor it out: ((8y + 9)(y + 1)).

So, the factored form of (8y^2 + 17y + 9) is ((8y + 9)(y + 1)).