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) = 6x^4 + x^3 - 8x^2 + 5x+6; k=1/2

Accepted Answer

Hey, everyone here we are asked to evaluate F of K using the remainder theorem. Here, our given equation is F of X is equal to six X to the fifth power minus 15 X cubed plus eight X squared minus 36. And our given value for K is two. Here we have four answer choice options. Answer a 74 answer B answer C 68 answer D zero. Here we first 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 is going to be equal to F of K. So here to find the remainder of our given function F of X, when our given value of K is two, all we need to find is F of K. So F of X is going to then be actually finding F of K and F of K tells us to find F of two since this is our given value. So all we need to do is substitute in two for X from our original function. So we now have six times two raised. To the power of five minus 15 times two, Q plus eight times two squared minus 36. So now just simplifying our expression here, we have six times two, raced to the fifth power which gives us 32. So we have six times 32 minus 15 times eight plus eight times four minus 36. And now multiply the terms together, we have first six times 32 which gives us 192. Then we have minus 120 then plus 32 lastly minus 36. And now just combining all of these terms here by either adding or subtracting, we get the final value for F of K which is 68. So with this final value that we obtained from substituting in F of X, we obtained our value for F F K which gives us answer choice C 68. 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) = 6x^4 + x^3 - 8x^2 + 5x+6; k=1/2

Key Concepts

Polynomial Functions

Remainder Theorem

Evaluation of Functions