Question

Divide the following polynomial, then place the answer in the proper location on the grid. Write your answer in order of descending powers of x.

(a^2n - a^n - 6) ÷ (a^n + 8)

Answer 1

The division of
`\(a^(2n) - a^n - 6\) by \(a^n + 8\) is \(a^n - 7\`

Let's divide the given polynomials:

`(a^(2n -a^n -6))/(a^n +8)`

Divide the leading term of the numerator by the leading term of the denominator:

`(a^(2n))/(a^n) = a^n` .

Multiply the entire denominator by the result from step 1 and subtract it from the numerator.

Bring down the next term and repeat steps 1 and 2 until you've gone through all the terms.

Here are the steps:

`& a^n & -1 & -6 \\`

`a^n + 8 & a^(2n) & & \\`

`& -a^(2n) & -8a^n & \\`

`& 0 & 7a^n & -6 \\\\& & \downarrow & \\\\ & & 7a^n & +56 \\\\& & -7a^n & -56 \\`

`& & 0 & 0\end{array} \]`

The result is
`\(a^n - 7\)`. Therefore, the division of
`\(a^(2n) - a^n - 6\) by \(a^n + 8\) is \(a^n - 7\`

Answer 2

Explanation:

x^4 - x^3 y + x^2 y^2 - x y^3 + y^4

2)

-1 + (2 + a^2 n)/(8 + a^n) i kinda guessed on this hope its right