Question

Given that f(x)=9x2−50 , apply the Remainder Theorem to find the remainder of (9x2−50)÷(x−73) .(1 point) Responses −50 negative 50 negative Start Fraction 203 over 3 End Fraction −1 negative 1 −29

Answer 1

To find the remainder of the polynomial \( f(x) = 9x^2 - 50 \) when divided by \( x - 73 \), we can apply the Remainder Theorem. The Remainder Theorem states that the remainder of the division of \( f(x) \) by \( x - c \) is equal to \( f(c) \).

In this case, we will evaluate \( f(73) \):

\[
f(73) = 9(73)^2 - 50
\]

First, calculate \( 73^2 \):

\[
73^2 = 5329
\]

Now substitute this back into the function:

\[
f(73) = 9(5329) - 50
\]

Now calculate \( 9(5329) \):

\[
9 \times 5329 = 47961
\]

Now, subtract 50:

\[
f(73) = 47961 - 50 = 47911
\]

Therefore, the remainder when \( 9x^2 - 50 \) is divided by \( x - 73 \) is \( 47911 \).

Since none of the responses you provided match this remainder, please check the options again. The remainder you are looking for is \( 47911 \).