Final answer:
The correct factorization for 63 and 49 is (x - 7)(x - 9), as factors of 63 include 7 and 9, which also relate to the factorization of 49 (which is 7 squared). Thus, option C is the correct answer.
Step-by-step explanation:
The student is asking about factoring the numbers 63 and 49. To factor these numbers, we want to find an expression with variables that can give us 63 and 49 when the expression is multiplied out. The common factor between the numbers 63 and 49 is 7, since 63 is 7 multiplied by 9, and 49 is 7 squared.
Looking at the provided options, we see that each one is a binomial expression, which means they are two terms separated by a plus or minus sign. To factor 63 and 49, we need the constants in the binomials to multiply to 63 and to add up in a way that could be squared to get 49. The only pair of factors of 63 in the options which could also relate to 49 (since 7 squared is 49) is 7 and 9.
As such, the correct option would be (x - 7)(x - 9), as this expression when expanded gives x times x (which is x squared), minus 7 times x, minus another 9 times x (which would be -16x when combined), and plus 63 (since -7 times -9 gives +63).