For each polynomial function, use the remainder theorem to fin...

Question

For each polynomial function, use the remainder theorem to find ƒ(k). ƒ(x) = x² + 4; k = 2i

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 64. And our given value for K is A I. Here we have four answer choice options, answer a zero, answer B six plus eight, I answer C A minus six I and answer D six minus eight I. So to solve this problem or 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 is equal to F of K. So to find F F K, all we need to do is substitute in the given value for F F K into F of X. So we have F of X is going to be equal to F of K. And we are given that K is A I. So we're actually trying to find F of A I. So this means that we just need to substitute in A I for X from our original function. So instead of X squared, we have the quantity of A I squared then just plus 64. And now we just need to simplify to find our value of F F K. OK. So simplifying we have 64 I squared plus 64. And now we need to recall that I squared is equivalent to negative one. So we actually have 64 times negative one plus 64. Simplifying further, we have negative 64 plus 64 adding these two values, they both cancel and we just get zero. So we find here that our value for F of K is just zero. So with this value for F F K, which we found by substituting in A I for X from our original function, we are left with answer choice A where our solution is just 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) = x² + 4; k = 2i

Key Concepts

Polynomial Functions

Remainder Theorem

Complex Numbers

For each polynomial function, use the remainder theorem to find ƒ(k). ƒ(x) = x2 + 4; k = 2i

Key Concepts

Polynomial Functions

Remainder Theorem

Complex Numbers

For each polynomial function, use the remainder theorem to find ƒ(k). ƒ(x) = x² + 4; k = 2i