Question

Consider the function f(x)=x³ 2x²−18x 490. what is the remainder if f(x) is divided by (x−11)?

Answer 1

To find the remainder of the function f(x) = x³ + 2x² − 18x + 490 when divided by (x - 11), we use the Remainder Theorem and calculate f(11), which yields a remainder of 1865.

Step-by-step explanation:

The question seems to refer to the polynomial division where you want to find the remainder of the function f(x) = x³ + 2x² − 18x + 490 when divided by (x − 11). To find this remainder, you would typically use the Remainder Theorem, which states that the remainder of the division of a polynomial f(x) by a linear binomial (x − r) is equal to f(r). Therefore, to find the remainder when f(x) is divided by (x − 11), we calculate f(11).

Let's compute:

• f(11) = 11³ + 2(11)² − 18(11) + 490
• f(11) = 1331 + 2(121) − 198 + 490
• f(11) = 1331 + 242 − 198 + 490
• f(11) = 1865

Thus, the remainder when f(x) is divided by (x − 11) is 1865.