54.4k views
1 vote
If f(x) = x^4-5x^3-5, then what is the remainder when f(x) is divided by x-6?

User Matuku
by
8.2k points

1 Answer

5 votes

Final answer:

Using the Remainder Theorem, the remainder when f(x) = x^4 - 5x^3 - 5 is divided by x - 6 is calculated by plugging 6 into the function, yielding a remainder of 211.

Step-by-step explanation:

To find the remainder when the function f(x) = x^4 - 5x^3 - 5 is divided by x - 6, we can use the Remainder Theorem. According to the theorem, if a polynomial f(x) is divided by x - a, the remainder is f(a). Therefore, to find the remainder of f(x) divided by x - 6, we need to calculate f(6).

Substituting 6 into the function, we get:

f(6) = 6^4 - 5(6)^3 - 5

f(6) = 1296 - 5(216) - 5

f(6) = 1296 - 1080 - 5

f(6) = 216 - 5

f(6) = 211

Therefore, the remainder when f(x) is divided by x - 6 is 211.

User Oyo
by
8.1k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories