What is the quotient represented by the expression 8w^2 - 20w - 12/2w+1 for all values of w where the expression is defined?

Question

A. 4w+12
B. 4w-12
C. w-3
D. w+3

Answer 1

To find the quotient, we need to perform polynomial long division.

First, we rewrite the expression in expanded form:
8w^2 - 20w - 12 / 2w + 1 can be rewritten as:
(8w^2 - 20w - 12) / (2w + 1)

Now, perform polynomial long division:
```
4w - 12
_________________________________
2w + 1 | 8w^2 - 20w - 12
- (8w^2 + 4w)
________________
-24w - 12
- (-24w - 12)
_____________
0

```

So, the quotient represented by the expression 8w^2 - 20w - 12 / 2w + 1 is 4w - 12.

Therefore, the answer is B. 4w-12.