The expression Q(b,x) = b(x+3) + x(x+3) + 4(x+3) is factorized by taking out the common factor (x+3), resulting in the factorized form (x+3)(b + x + 4).
The question involves factorizing a given expression which is a typical problem in algebra, a branch of mathematics. The expression provided is Q(b,x) = b(x+3) + x(x+3) + 4(x+3). To factorize this expression, we look for common factors in each term. Here, we can see that each term has a common (x+3) factor. So, we can take (x+3) out as a common factor, resulting in:
Q(b,x) = (x+3)(b + x + 4)
This is the factorized form of the given expression. In general, when dealing with quadratic equations like ax² + bx + c = 0, the solutions or roots can be found using the quadratic formula. However, in this particular case, we were able to factorize by grouping and taking out the common factor.