Finnd the quotient and remainder when F(x)=6x^3+4x^2-x+5 divided by 3x^2+2x+1 using the long division method

Answer 1

Let's perform the long division:

2x + 1
_______________
3x^2+2x+1 | 6x^3+4x^2-x+5

To start the division, we divide the first term of the dividend by the first term of the divisor:

2x + 1
____________________
3x^2+2x+1 | 6x^3+4x^2-x+5
- (6x^3 + 4x^2 + 2x^2)
________________________
-x+5

Now, we bring down the next term, -x, and divide it by the first term of the divisor:

2x + 1
_____________________
3x^2+2x+1 | 6x^3+4x^2-x+5
- (6x^3 + 4x^2 + 2x^2)
________________________
-x+ 5
-(-x+0)
__________________
5

The quotient is 2x + 1 and the remainder is 5.