Consider the following division of polynomials. x^24+x^3+7x^2-6x+8 divide by x^2+2x+8 a) use long division to determine the quotient of the polynomials. show all of your work for full credit. b) use mathematical methods to prove your answer. show all of your work for full credit.

 x²  -x + 1   Quotient

Step-by-step explanation:

Given in the question,

the numerator = x^4 + x³ + 7x² - 6x + 8

the denominator = x² + 2x + 8

Dividing :

x^4+x^3+7x^2-6x+8  ("Dividend")

By :

 x2+2x+8    ("Divisor")

                                                                 x²  -x + 1                      Quotient

dividend          x² + 2x + 8     | x^4 +   x^3 +  7x² -6x + 8

divisor  *x²                                  x^4 + 2x^3 + 8x²

remainder                                                 -x³   - x²   -6x + 8

divisor  * -x1                                              -x³  -2x² . -8x  

remainder                                                           x²   +2x   +8

divisor  *1                                                            x²   +2x   +8

remainder                                                                          0

B)

(x²  -x + 1)   (x² + 2x + 8)    

= x^4 +   x^3 +  7x² -6x + 8

hence proved 

domain is all the x values included in the

0 ≤ x ≤ 2

range is all the y values of the graph

-2 ≤ y ≤ 2

***keep in mind that there are different ways to show domain and range

hope this !

~just a girl in love with shawn mendes

answer: 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

step-by-step explanation: