Divide: (x^(4)+8x^(3)-10x^(2)-48 x-17)÷(x^(2)-6)

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Use Polynomial Long Division: To divide the polynomial $x^4 + 8x^3 - 10x^2 - 48x - 17$ by the binomial $x^2 - 6$, we will use polynomial long division.Divide Leading Terms: First, we divide the leading term of the dividend, $x^4$, by the leading term of the divisor, $x^2$, to get $x^2$. This will be the first term of our quotient.Subtract Result: Next, we multiply the entire divisor $x^2 - 6$ by $x^2$ and subtract the result from the dividend. $x^2 \cdot (x^2 - 6) = x^4 - 6x^2$. Subtracting this from the dividend gives us: $(x^4 + 8x^3 - 10x^2) - (x^4 - 6x^2) = 8x^3 + 4x^2 - 48x - 17$.Divide New Leading Term: Now, we divide the leading term of the new dividend, $8x^3$, by the leading term of the divisor, $x^2$, to get $8x$. This will be the next term of our quotient.Subtract Result Again: We multiply the entire divisor $x^2 - 6$ by $8x$ and subtract the result from the new dividend. $8x \cdot (x^2 - 6) = 8x^3 - 48x$. Subtracting this from the new dividend gives us: $(8x^3 + 4x^2 - 48x) - (8x^3 - 48x) = 4x^2 - 17$.Divide Remaining Term: Finally, we divide the leading term of the remaining dividend, $4x^2$, by the leading term of the divisor, $x^2$, to get $4$. This will be the last term of our quotient.Subtract Final Result: We multiply the entire divisor $x^2 - 6$ by $4$ and subtract the result from the remaining dividend. $4 \cdot (x^2 - 6) = 4x^2 - 24$. Subtracting this from the remaining dividend gives us: $(4x^2 - 17) - (4x^2 - 24) = 7$.Determine Quotient and Remainder: The remainder is $7$, which cannot be divided further by $x^2 - 6$ since it is of lower degree. Therefore, the quotient is $x^2 + 8x + 4$ with a remainder of $7$.

Divide: $(x^{4}+8x^{3}-10x^{2}-48x-17)\div(x^{2}-6)$

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Divide: (x4+8x3−10x2−48x−17)÷(x2−6)(x^{4}+8x^{3}-10x^{2}-48x-17)\div(x^{2}-6)(x4+8x3−10x2−48x−17)÷(x2−6)

Divide: $(x^{4}+8x^{3}-10x^{2}-48x-17)\div(x^{2}-6)$