Question

Given that f(x)=9x^2−50, apply the Remainder Theorem to find the remainder of (9x^2−50)÷(x−73).

Answer 1

The Remainder Theorem states that if a polynomial \( f(x) \) is divided by \( x - c \), the remainder of that division is equal to \( f(c) \).

In your case, the polynomial is \( f(x) = 9x^2 - 50 \), and you are dividing by \( x - 73 \). Here, \( c = 73 \).

To find the remainder, we calculate \( f(73) \):

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

First, calculate \( 73^2 \):

\[
73^2 = 5329
\]

Now substitute this value back into the function:

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

Now, multiply:

\[
9 \times 5329 = 47961
\]

Then subtract 50:

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

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