Use long division to divide. Express any numbers as integers or simplified fractions. (x^5-2x^4+20x^3-15x+18)div (x^2-3)=square

1. Set up the division<br /> Arrange $x^5 - 2x^4 + 20x^3 - 15x + 18$ under the long division bar and $x^2 - 3$ outside.<br /><br />2. Divide the leading terms<br /> Divide $x^5$ by $x^2$ to get $x^3$. Multiply $x^3$ by $(x^2 - 3)$, resulting in $x^5 - 3x^3$. Subtract from the original polynomial.<br /><br />3. Subtract and bring down next term<br /> Subtract $x^5 - 3x^3$ from $x^5 - 2x^4 + 20x^3$, resulting in $-2x^4 + 23x^3$. Bring down $-15x$.<br /><br />4. Repeat division process<br /> Divide $-2x^4$ by $x^2$ to get $-2x^2$. Multiply $-2x^2$ by $(x^2 - 3)$, resulting in $-2x^4 + 6x^2$. Subtract from current polynomial.<br /><br />5. Subtract and bring down next term<br /> Subtract $-2x^4 + 6x^2$ from $-2x^4 + 23x^3 - 15x$, resulting in $23x^3 - 6x^2 - 15x$. Bring down $+18$.<br /><br />6. Continue division<br /> Divide $23x^3$ by $x^2$ to get $23x$. Multiply $23x$ by $(x^2 - 3)$, resulting in $23x^3 - 69x$. Subtract from current polynomial.<br /><br />7. Subtract and finalize remainder<br /> Subtract $23x^3 - 69x$ from $23x^3 - 6x^2 - 15x + 18$, resulting in $-6x^2 + 54x + 18$. <br /><br />8. Final division step<br /> Divide $-6x^2$ by $x^2$ to get $-6$. Multiply $-6$ by $(x^2 - 3)$, resulting in $-6x^2 + 18$. Subtract from current polynomial.<br /><br />9. Conclude division<br /> Subtract $-6x^2 + 18$ from $-6x^2 + 54x + 18$, resulting in $54x$. This is the remainder.