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 −2033 negative Start Fraction 203 over 3 End Fraction −1 negative 1 −29

Answer 1

To find the remainder of \( f(x) = 9x^2 - 50 \) when divided by \( x - 73 \) using the Remainder Theorem, we can evaluate \( f(73) \).

Let's calculate \( f(73) \):

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

First, calculate \( 73^2 \):

\[ 73^2 = 5329 \]

Now substitute this back into \( f(x) \):

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

Now calculate \( 9 \times 5329 \):

\[ 9 \times 5329 = 47961 \]

Now, subtract 50:

\[ 47961 - 50 = 47911 \]

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

It seems that 47911 is not one of the provided responses. Let's double-check our calculations methodically.

1. Calculate \( 73^2 \): \[ 73 \times 73 = 5329 \]

2. Thus, \( 9(5329) \): \[ 9 \times 5329 = 47961 \]

3. Finally: \[ 47961 - 50 = 47911 \]

If there's a mismatch in the responses provided, verify if there might have been a misunderstood division or context leading to the options. That said, based on the calculation, the correct value for the remainder should be \( 47911 \).

If we were working with \( 9(73)^2 - 50 \) specifically, this does lead to a remainder of \( 47911 \) by normal standards of polynomial division and evaluation. Ensure setup context matches continuation queries as the provided options do not include the correct remainder found.