Question
Given that f(x) = 9x2−50,
apply the Remainder Theorem to find the remainder of (9x2−50)÷(x − 73).
(1 point)
Responses
-50
-50
-1
-1
-2033
- 203 thirds
-29
apply the Remainder Theorem to find the remainder of (9x2−50)÷(x − 73).
(1 point)
Responses
-50
-50
-1
-1
-2033
- 203 thirds
-29
Answers
GPT-4o mini
To apply the Remainder Theorem, we need to evaluate the function \( f(x) = 9x^2 - 50 \) at \( x = 73 \). The Remainder Theorem states that the remainder of dividing a polynomial \( f(x) \) by \( x - c \) is equal to \( f(c) \).
Here, \( c = 73 \).
Now, let's calculate \( f(73) \):
\[
f(73) = 9(73)^2 - 50
\]
First, calculate \( 73^2 \):
\[
73^2 = 5329
\]
Now, substitute back into the function:
\[
f(73) = 9(5329) - 50
\]
Calculating \( 9 \times 5329 \):
\[
9 \times 5329 = 47961
\]
Now, subtract 50:
\[
f(73) = 47961 - 50 = 47911
\]
Thus, the remainder when \( 9x^2 - 50 \) is divided by \( x - 73 \) is:
\[
\boxed{47911}
\]
Since none of the answer options provided appear to align with the calculated result, it seems that there may have been a misunderstanding or misprint in the choices given.
Here, \( c = 73 \).
Now, let's calculate \( f(73) \):
\[
f(73) = 9(73)^2 - 50
\]
First, calculate \( 73^2 \):
\[
73^2 = 5329
\]
Now, substitute back into the function:
\[
f(73) = 9(5329) - 50
\]
Calculating \( 9 \times 5329 \):
\[
9 \times 5329 = 47961
\]
Now, subtract 50:
\[
f(73) = 47961 - 50 = 47911
\]
Thus, the remainder when \( 9x^2 - 50 \) is divided by \( x - 73 \) is:
\[
\boxed{47911}
\]
Since none of the answer options provided appear to align with the calculated result, it seems that there may have been a misunderstanding or misprint in the choices given.