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^2 + 5x+6; 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 X squared plus 25 X plus 136. And our given value for K is negative. A here we have four answer choice options, answer a zero answer B 40 answer C 400 answer choice D 80. So here before we evaluate F of K, 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 for this expression is going to be F of K. So now, here we are trying to evaluate F of K, which means we are finding the remainder for when our given function F of X is divided by X minus K. So to begin finding F F K, we first take our function F of X and we substitute in K for X. So our given value for K is negative eight, which means that we are actually substituting in negative eight. Or in other words, we need to find F of negative A. So again, we need to substitute in negative 84 X from our original function. And so we get the quantity of negative eight squared plus 25 times negative eight plus 136. Now, we just need to simplify this expression. So we have 64 minus 200 plus 136. And now combining all of these terms by adding or subtracting accordingly, we see that we get a final value of zero. So we get F of K is equal to zero, which tells us that our remainder is zero for when we take our given function F of X and divide it by X minus negative eight. So with this remainder of zero, we are left with answer choice. A where our final solution is zero. 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^2 + 5x+6; k = -2

Key Concepts

Polynomial Functions

Remainder Theorem

Evaluating Functions