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) = x^3 - 4x^2 + 2x+1; k = -1

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 negative X cubed plus five, X squared minus eight X plus 12. And our given value for K is negative three. Here we have four answer choice options. Answer a 54 answer B answer C zero and answer D six. So here, before we evaluate F of K, we need to recall the remainder theorem which states that if a polynomial F of X is, is divided by the expression X minus K, then we know that the remainder R is going to be equal to F of K. So in other words, we are finding or evaluating F F K, which means we are finding the remainder for when our given function is divided by X minus negative three. So we can start by taking our function F of X. And we know we need to find F of K. So we substitute in K four X, which really means that we need to substitute in the given value for K which is negative three. So here we are finding F of negative three by again, substituting in negative 34 X from our original function. So in doing this, we have negative one times the quantity of negative three Q plus five times the quantity of negative three squared minus eight times negative three plus 12. Now all we need to do is simplify our expression here. So we get seven plus 45 plus 24 plus 12. And now adding all of these terms, we see that our final value for F of K or F of negative three is equal to 108. So from this value of F of K, we have found the remainder for when F of X is divided by X minus negative three. So with this final value of 108 we are left with B with our answer being 108. 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) = x^3 - 4x^2 + 2x+1; k = -1

Key Concepts

Polynomial Functions

Remainder Theorem

Function Evaluation