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)

Question

asked Oct 12, 2019 173k views

2 Answers

Alex Pertsev · Answer 1 · 2019-10-13T12:21:35+0000

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\$

FelHa · Answer 2 · 2019-10-18T01:53:27+0000

Answer:

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