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

Question

(9x^2 - 50) ÷ (x - 7/3). (1 point)
What is the correct answer and why

Answer 1

To apply the Remainder Theorem, we need to evaluate the polynomial \( f(x) = 9x^2 - 50 \) at \( x = \frac{7}{3} \).

The Remainder Theorem states that the remainder of the division of a polynomial \( f(x) \) by \( x - c \) is equal to \( f(c) \). In this case, we have \( c = \frac{7}{3} \).

Now, let's substitute \( x = \frac{7}{3} \) into \( f(x) \):

\[ f\left(\frac{7}{3}\right) = 9\left(\frac{7}{3}\right)^2 - 50 \]

Calculating \( \left(\frac{7}{3}\right)^2 \):

\[ \left(\frac{7}{3}\right)^2 = \frac{49}{9} \]

Now substituting this back into our function:

\[ f\left(\frac{7}{3}\right) = 9 \cdot \frac{49}{9} - 50 = 49 - 50 = -1 \]

Thus, the remainder when \( 9x^2 - 50 \) is divided by \( x - \frac{7}{3} \) is \(-1\).

The correct answer is \(-1\).