Answer:
s(2r + 2s) or 2s(r + s)
Explanation:
To factor -10r^2-11sr+6s^2, we need to find two binomials that when multiplied together give us the original expression.
First, we need to find two numbers that multiply to give -60s^2 (the product of the coefficients of the first and last term) and add to give -11s (the coefficient of the middle term). These numbers are -5s and -6s.
We can now split the middle term -11sr into -5sr - 6sr and rewrite the original expression as:
-10r^2 - 5sr - 6sr + 6s^2
Now we can factor by grouping:
(-10r^2 - 5sr) + (-6sr + 6s^2)
Factor out -5s from the first group, and 6s from the second group:
-5s(2r + s) + 6s(1r - s)
Now we have a common factor of (2r + s) - (1r - s):
(-5s + 6s)(2r + s - 1r + s)
Simplifying this expression gives us the final factorization:
s(2r + 2s) or 2s(r + s)