Question

What is the quotient (2x4 – 3x3 – 3x2 + 7x – 3) ÷ (x2 – 2x + 1)?

Answer 1

2x²+x-3. The quotient resulting of the division of the polynomial
`(2x^(4) -3x^(3) -3x^(2) +7x-3)` ÷
`(x^(2) -2x+1)` is 2x²+x-3.

In order to find the quotient we have to apply the division of the polynomial
`(2x^(4) -3x^(3) -3x^(2) +7x-3)` ÷
`(x^(2) -2x+1)` is 2x²+x-3.

We divide the first monomial of the dividend
`(2x^(4))` between the first monomial of the divisor
`(x^(2))`.

(2x^{4})÷
`(x^(2))`=
`2x^(2)`

This result
`2x^(2)` is put under the box and we multiply it by each term of the divisor polynomial and the result is subtracted in the polynomial dividend:

2x^4 -3x^3 -3x^2 +7x -3 ║ x^2 -2x +1

-2x^2+4x^3 -2x^2 ║ 2x^2+x-3 -----------> This is the quotient

x^3 -5x^2 +7x -3

-x^3 +2x^2 - x +0

-3x^2 +6x -3

3x^2 -6x +3

0

Answer 2

The correct answer is,

2x² + x - 3

Explanation:

It is given that,

(2x4 – 3x3 – 3x2 + 7x – 3) ÷ (x2 – 2x + 1)

To find the quotient

2x² + x - 3

x² - 2x + 1 | 2x4 – 3x3 – 3x2 + 7x – 3

2x⁴ - 4x³ + 2x²

x³ - 5x² + 7x

x³ - 2x² + x

-3x² + 8x - 3

-3x² + 6x - 3

2x

Therefore the quotient is 2x² + x - 3