Question

What is the remainder when the function f(x)=x⁴−3x³+7x−1 is divided by (x−2)?

Answer 1

To find the remainder when the function f(x)=x⁴−3x³+7x−1 is divided by (x−2), we can use synthetic division. The remainder is -9.

Step-by-step explanation:

To find the remainder when the function f(x)=x⁴−3x³+7x−1 is divided by (x−2), we can use synthetic division.

Let's write the function in descending order of powers of x: f(x) = x⁴ - 3x³ + 0x² + 7x - 1.

Next, we set up the synthetic division by writing (x−2) as a divisor: 2| 1 -3 0 7 -1.

Performing the synthetic division, we get a remainder of -9.

Therefore, the remainder when the function f(x)=x⁴−3x³+7x−1 is divided by (x−2) is -9.