Question

How to factor -10r^2-11sr+6s^2

Answer 1

Answer: -(5r-2s)(2r+3s)

Step-by-step explanation: First you factor out the negative 1 and you get -(10r^2 + 11sr -6s^2). Then you factor it to get -(5r-2s)(2r+3s).

Answer 2

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)