Question

Divide f(x) by d(x). Your answer

should be in the following format:
R(x)
f(x) = Q(x) + d(x)
f(x) = x³+4x²+7x-9
d(x)=x+3
R(x) = [?]
Only enter the R(x) term.

Answer 1

To divide f(x) by d(x), we need to perform polynomial long division:

```
_________
x + 3 | x³ + 4x² + 7x - 9
```

To start the division, we divide the highest degree term of f(x) by the highest degree term of d(x), which gives us x². We then multiply x² by d(x), which is x + 3, and subtract it from f(x):

```
x²
__________
x + 3 | x³ + 4x² + 7x - 9
- (x³ + 3x²)
__________
x² + 7x - 9
```

Now we repeat the process with the new polynomial x² + 7x - 9:

```
x² + 7x
__________
x + 3 | x³ + 4x² + 7x - 9
- (x³ + 3x²)
__________
x² + 7x - 9
- (x² + 3x)
__________
4x - 9
```

We are left with the remainder 4x - 9. Therefore, R(x) = 4x - 9.