Find the values of a, b and c in the equation: (5x + 3)(ax + b) = 10x^2 + 11x + c.

We can go about solving this problem by equating the coefficients of x^2, x, and the constant c. First of all, we must expand the bracket (5x + 3)(ax + b). One helpful way of doing this correctly is the FOIL method: First, Outer, Inner, Last. So to expand the bracket we multiply the First number in each bracket, the values on the Outside of the equation, the values on the Inside of the equation and the Last values in each bracket. We then add the values we get together. So we should have: F: 5x * ax = 5ax^2, O: 5x * b = 5bx, I: 3 * ax = 3ax, L: 3 * b = 3b When added together we get 5ax^2 + (5b + 3a)x + 3b. Now we can equate this to 10x^2 + 11x + c. Comparing coefficients we see that - 5a = 10. By dividing both sides by 5 get a = 2. - 5b + 3a = 11. By substituting a = 2 into this formula we get that b = 1. - 3b = c. By substituting b = 1 we find that c = 3. Now we have solved the question!