Which is a factor of 6a2 plus 5ab - 6b2?

Considering the minus sign between 5ab and 6b2 then we have the polynomial as 6a2 + 5ab - 6b2. The polynomial is a quadratic polynomial.

Steps to factorize a quadratic polynomial:

1 - Multiply first term by third term. 6a2 x (-6b2) = -36a2b2

2 - If possible break the second term into two terms such that they multiple to -36a2b2. If not then it is factorized by Sridharacharya's formula.

5ab can be broken as 9ab + (-4ab).

These two terms multiply to give -36a2b2.

So we can write 6a2 + 5ab - 6b2 = 6a2 + 9ab + (-4ab) - 6b2.

6a2 + 9ab - 4ab - 6b2 = 3a(2a + 3b) - 2b(2a + 3b) = (2a + 3b)(3a - 2b).

So the factors are (2a + 3b) and (3a - 2b).