Answer: 3x + 1
Step-by-step explanation:
The given expression is
(3x^2 + 22x + 7)/(x + 7)
The first step is to factorize the numerator, (3x^2 + 22x + 7)
This is a quadratic expression. We would solve by applying the method of factorization. The first step is to multiply 3x^2 with 7. It becomes 21x^2. We would find two terms such that their sum or difference is 22x and their product is 21^2. The terms are 21x and x. By replacing 22x with 21x + x, we have
3x^2 + 21x + x + 7
We would factorize by groupin. we havve
3x(x + 7) + 1(x +7)
(3x + 1)(x + 7)
Thus the original expression becomes
(3x + 1)(x + 7)/(x + 7)
(x + 7) cancels out
it becomes 3x + 1