Certainly! Let's solve this step by step.
The problem states that a polynomial [tex]\( f(x) \)[/tex] has a remainder of 7 when divided by [tex]\( x - 7 \)[/tex].
To solve this, we can use the Remainder Theorem. The Remainder Theorem says that if a polynomial [tex]\( f(x) \)[/tex] is divided by [tex]\( x - c \)[/tex], the remainder of this division is [tex]\( f(c) \)[/tex].
In this case, [tex]\( f(x) \)[/tex] is being divided by [tex]\( x - 7 \)[/tex]. Thus, according to the Remainder Theorem, the remainder when [tex]\( f(x) \)[/tex] is divided by [tex]\( x - 7 \)[/tex] is [tex]\( f(7) \)[/tex].
We are given that this remainder is 7. Therefore, we can write:
[tex]\[ f(7) = 7 \][/tex]
So, the answer is
[tex]\[ f(7) = 7 \][/tex]
