Question

Find the remainder when f(x) = 2x³ + x² - 4x + 3 is divided by (x-3).

Answer 1

We can use synthetic division to find the remainder when f(x) is divided by (x-3):

```

3 | 2 1 -4 3

| 6 21 51

|----------------

| 2 7 17 54

```

Therefore, the remainder when f(x) is divided by (x-3) is 54.

Answer 2

To find the remainder when a polynomial is divided by a linear factor, we can use the remainder theorem. According to the remainder theorem, if a polynomial f(x) is divided by (x - a), the remainder is equal to f(a).

In this case, we want to find the remainder when f(x) = 2x³ + x² - 4x + 3 is divided by (x - 3). To do that, we substitute x = 3 into the polynomial:

f(3) = 2(3)³ + (3)² - 4(3) + 3

= 2(27) + 9 - 12 + 3

= 54 + 9 - 12 + 3

= 54 + 9 - 9

= 54

Therefore, the remainder when f(x) is divided by (x - 3) is 54.