For each polynomial function, use the remainder theorem to find ƒ...

Question

For each polynomial function, use the remainder theorem to find ƒ(k).
ƒ(x) = 2x^2 - 3x-3; k = 2

Accepted Answer

Hey, everyone here we are asked to evaluate F of K using the remainder theorem. Here, our given function is F of X is equal to five X squared minus eight X plus seven. And our given and value four K is six. Here we have four answer choice options, answer a zero, answer B 139 answer C 235 and answer D 42. Now, before we begin evaluating for F F K, we want to recall the remainder theorem which states that if a polynomial F of X is divided by the expression X minus K, then we know that the remainder is going to be equal to F of K. So here we are finding the remainder F of K for when our given function F of X is divided by X minus K or in our case X minus six. So to find F of K, we just need to take our function F of X and substitute in K four X. So we are given the value of 64 K. So we are actually just finding F of six, which is found by just substituting in 64 X from our original function. So substituting in six, we have five times six squared minus eight times six plus seven. And now we just want to simplify our expression. So we have 180 minus plus seven. And now adding or subtracting our terms accordingly, we get the final value for F of K or F of six, which ends up being 139. So with this value we obtained for F F K, we know that when we take our original function F of X and divide it by X minus six, we get this remainder of 139. So with this remainder value, we have found our value for F F K leaving us with answer choice B 139. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

For each polynomial function, use the remainder theorem to find ƒ(k). ƒ(x) = 2x^2 - 3x-3; k = 2

Key Concepts

Polynomial Functions

Remainder Theorem

Evaluation of Functions