Question

2x^ 3 +17x^ 2 +20x+6 is divided by 2 x + 1

Answer 1

`\sf x^ 2 +17x^ 2 +20x+6`

Explanation:

`\sf (2x^ 3 +17x^ 2 +20x+6)/( 2 x + 1)`

2x³/2x = x²

`\sf (x^ 2 +17x^ 2 +20x+6)/( 1)`

`\sf x^ 2 +17x^ 2 +20x+6`

Answer 2

The quotient is x^2 + 9x + 6 with a remainder of 6.

Explanation:

I used the polynomial long division method to divide the polynomial 2x^3 + 17x^2 + 20x + 6 by 2x + 1.

1. First, I divided the leading coefficient of the dividend (2x^3) by the leading coefficient of the divisor (2x). This gave me x^2 as the first term of the quotient.
2. Next, I multiplied the divisor (2x + 1) by the first term of the quotient (x^2) to get 2x^3 + x^2.
3. I then subtracted this product from the dividend (2x^3 + 17x^2 + 20x + 6) to get 17x^2 + 20x + 6 as the new dividend.
4. I then brought down the next term of the dividend (17x^2) and divided it by the leading coefficient of the divisor (2x) to get 8.5x as the next term of the quotient.
5. I then multiplied the divisor (2x + 1) by this term (8.5x) to get 17x^2 + 8.5x.
6. I subtracted this product from the new dividend (17x^2 + 20x + 6) to get 0.5x + 6 as the new dividend.
7. I brought down the next term of the dividend (0.5x) and divided it by the leading coefficient of the divisor (2x) to get 0.25x as the next term of the quotient.
8. I multiplied the divisor (2x + 1) by this term (0.25x) to get 0.5x.
9. I subtracted this product from the new dividend (0.5x + 6) to get 6 as the remainder.

So the quotient is x^2 + 8.5x + 0.25x which simplifies to x^2 + 9x + 6 and the remainder is 6.