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 + 8x^2 + 63; k=4

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 two X cubed plus 11 X squared plus six. And our given value for K is two. Here we have four answer choice options, answer a zero answer B 84 answer C 76 answer D 44. So here, before evaluating F F K, we need 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 R is going to be equal to F of K. So here we are finding or evaluating F F K, which means we are finding the remainder for when our given function F of X is divided by X minus K. So we can take our given function F of X. And again, we are trying to find F of K. So we just substitute in K for X, which means we actually substitute in the value of two, which is given for K. So in other words, we are finding F of two. So now substituting in two for X from our original function, we have negative two times two cubed plus 11 times two squared plus 16. And now from here, all we need to do is just start simplifying. So from our first term here we get negative 16, we then have plus 44 lastly plus 16. And simplifying further, we find that our final value for F of K is just 44. And so this value for F F K also tells us that the remainder for when our given function F of X is divided by X minus two, we get the remainder of 44. So with this value that we obtained for F F K, we are left with answer choice D where our final answer is 44. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

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For each polynomial function, use the remainder theorem to find ƒ(k). ƒ(x) = - x^3 + 8x^2 + 63; k=4