Question

If f(x) = 4x^5+3 then what is the remainder when f(x) is divided by x-2

Answer 1

131

Explanation:

2 | 4 0 0 0 0 3

_____8 16 32 64 128__

4 8 16 32 64 | 131

Using synthetic division, we can see that the remainder when f(x) is divided by x-2 is 131.

Alternatively, to find the remainder when dividing f(x) by (x-2), we can use the remainder theorem. The remainder theorem states that if a polynomial f(x) is divided by (x - c), the remainder is equal to f(c).

In this case, we have f(x) = 4x^5 + 3 and we want to find the remainder when f(x) is divided by (x - 2). Therefore, we substitute x = 2 into f(x) to find the remainder.

f(2) = 4(2)^5 + 3

= 4(32) + 3

= 128 + 3

= 131

Hence, the remainder when f(x) is divided by (x - 2) is 131.

Answer 2

We can use polynomial long division to divide f(x) by x - 2.

```
4x^4 + 8x^3 + 16x^2 + 32x + 67
_____________________________________________
x - 2 | 4x^5 + 0x^4 + 0x^3 + 0x^2 + 0x + 3
- (4x^5 - 8x^4)
---------------
8x^4
- 8x^4 + 16x^3
---------------
16x^3
- 16x^3 + 32x^2
----------------
32x^2
- 32x^2 + 64x
--------------
67
```

Therefore, the remainder when f(x) is divided by x - 2 is 67.