Answer:
To solve the equation Ax^2 + bx + c = (5x - 6)(2x - 1), we need to expand the right side of the equation using the distributive property.
(5x - 6)(2x - 1) can be expanded as follows:
(5x)(2x) + (5x)(-1) + (-6)(2x) + (-6)(-1)
Which simplifies to:
10x^2 - 5x - 12x + 6
Combining like terms, we get:
10x^2 - 17x + 6
So, the expanded form of (5x - 6)(2x - 1) is 10x^2 - 17x + 6.
Now, we can equate this expression to the left side of the equation:
Ax^2 + bx + c = 10x^2 - 17x + 6
By comparing the coefficients of corresponding powers of x on both sides, we can determine the values of A, b, and c.
Comparing the coefficient of x^2:
A = 10
Comparing the coefficient of x:
b = -17
Comparing the constant terms:
c = 6
Therefore, the values of A, b, and c are A = 10, b = -17, and c = 6.
In summary, the values of A, b, and c for the equation Ax^2 + bx + c = (5x - 6)(2x - 1) are A = 10, b = -17, and c = 6.