The expression (2x+a) (3x-b) is the complete factorization of 6x^2+x-12. What must be the respective values of a and B?
To find the values of a and b, we need to compare the given expression (2x+a)(3x-b) with the given polynomial 6x^2+x-12.
First, we expand the expression (2x+a)(3x-b):
(2x+a)(3x-b) = 6x^2 - 2bx + 3ax - ab
Now, comparing this with the polynomial 6x^2+x-12:
6x^2 - 2bx + 3ax - ab = 6x^2 + x - 12
By comparing the coefficients of like terms, we can set up two equations:
-2b = 1 (for the x term)
3a = 0 (for the constant term)
From the second equation, we find that a = 0.
Substituting a = 0 into the first equation, we find that -2b = 1, which implies b = -1/2.
Therefore, the values of a and b are a = 0 and b = -1/2.