Final answer:
The expression (7a^2 - 51a + 17) divided by (a - 7) is simply 7a, as (a - 7) is a factor of the dividend, resulting in no remainder.
Step-by-step explanation:
To divide the expression (7a^2 - 51a + 17) by (a - 7), we can apply polynomial long division or synthetic division since we are dividing by a linear binomial of the form (a - b). However, an even simpler method is to notice that when a is substituted by 7, the divisor (a - 7) becomes zero. This implies we can use the remainder theorem which states that when a polynomial f(a) is divided by (a - b), the remainder is f(b). Substituting 7 into the dividend gives us 7(7)^2 - 51(7) + 17 which simplifies to 0, indicating that (a - 7) is a factor of 7a^2 - 51a + 17.
Since (a - 7) is a factor, we can expect the result to be a polynomial of one degree lower than the dividend, hence of the form 7a + c, where c is a constant. To find c, we could perform long division or synthetic division. Given the possible options provided and the fact that we have found no remainder, we can deduce that the quotient will not include a constant term, so the answer must be 7a. Therefore, we can conclude that the division of the given expression by (a - 7) is 7a.
To ensure the result is reasonable it should be noted that this question is a pure division without requiring a remainder or additional terms.