Answer:
By using remainder theorem when divided by x-6 the value of f(6) = 4 .
Explanation:
If F(x) has a remainder of 4 when divided by x−6, we can express this as:
F(x)=(x−6)Q(x)+4
where Q(x) is the quotient. The remainder theorem states that if you substitute the root of the divisor (in this case, 6) into the polynomial, you get the remainder. Therefore:
F(6) = (6−6) Q (6) + 4
Simplifying, we find that
F(6) = 4. This means that when you substitute 6 into the polynomial
F(x), you get a remainder of 4.
It's important to note that this result doesn't depend on the specific form of F(x) or Q (x), only on the fact that the remainder is 4 when divided by
x−6.
In conclusion, F(6)=4 based on the remainder theorem.