Find the quotient and remainde when Fx=4x^3+3x^2-2x is divided by 2x+l

Answer 1

To find the quotient and remainder when F(x) = 4x^3 + 3x^2 - 2x is divided by 2x + 1, we can use polynomial long division.

2x^2 - x + 3
_____________________
2x + 1 | 4x^3 + 3x^2 - 2x + 0

To start, we divide the leading term of F(x) by the leading term of 2x + 1, which is 2x^2.

2x^2
__________
2x + 1 | 4x^3 + 3x^2 - 2x + 0

Next, we multiply (2x^2) by (2x + 1) to get 4x^3 + 2x^2. We subtract this from the original polynomial:

2x^2 - x + 3
_____________________
2x + 1 | 4x^3 + 3x^2 - 2x + 0
- (4x^3 + 2x^2)
________________
x^2 - 2x

We now bring down the next term, which is -2x:

2x^2 - x + 3
_____________________
2x + 1 | 4x^3 + 3x^2 - 2x + 0
- (4x^3 + 2x^2)
________________
x^2 - 2x
- (x^2 - 2x)
___________
0

Since we have no more terms to bring down and continue dividing, our remainder is 0. Therefore, the quotient when F(x) is divided by 2x + 1 is 2x^2 - x + 3, and the remainder is 0.