Question

Divide the following polynomials and then complete the quotient. Write your answer in order of decreasing powers of x .

(32x^8 - 8x^6 + 28x^4) / 4x^4

Answer 1

We need to perform division of polynomials such as the solution is shown below:
( 32x8 - 8x6 + 28x4) / 4x4
(32x8 / 4x4)  - ( 8x6 / 4x4 )  + (28x4 / 4x4)
8x4  - 2x2 + 7
The power of the result was already arranged in descending order. 

The answer is "8x4 - 2x2 + 7 ".

Answer 2

Answer:  The quotient in order of decreasing powers of x is

$Q=8x^4-2x^2+7.$

Step-by-step explanation:  We are given to divide the following polynomials and to complete the quotient :

$Q=\dfrac{32x^8-8x^6+28x^4}{4x^4}~~~~~~~~~~~~~~~~~~~(i)$

We are to write the answer in order of decreasing powers of x.

From (i), we have

$Q\\\\=\dfrac{32x^8-8x^6+28x^4}{4x^4}\\\\\\=\dfrac{4x^4(8x^4-2x^2+7)}{4x^4}\\\\=8x^4-2x^2+7.$

Thus, the required quotient in order of decreasing powers of x is

$Q=8x^4-2x^2+7.$