Question

The quotient of (x^4-3x^2+4x-3) and a polynomial is (x^2+x-3) what is the polynomial

Answer 1

`\displaystyle \boxed{x^2 - x + 1}`

Step-by-step Step-by-step explanation:

Divide the leading coefficients of the divisor and dividend:

`\displaystyle x^2 = (x^4)/(x^2) \\ \\ x^4 + x^3 - 3x^2 = x^2[x^2 + x - 3]`

`\displaystyle -x^3 + 4x - 3 = -[x^4 + x^3 - 3x^2] + [x^4 - 3x^2 + 4x - 3]`

Now you have this:

`\displaystyle (-x^3 + 4x - 3)/(x^2 + x - 3) \\ \\ -x = \ -(x^3)/(x^2) \\ \\ 1 = (-3)/(-3)`

Altogether, you have this:

`\displaystyle \boxed{x^2 - x + 1}`

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