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 

x =-.20752

step-by-step explanation:

4^(x+2)=12

4^(x+2)=12

take the log base 4 on each side

log 4 (4^(x+2) = log 4(12)

we know log b(a^y) = y log b (a)

(x+2) log 4(4) = log 4 (12)

x+2 = log 4 (12)

we know   logb c = loga c/loga b

we want to convert to base 10   so a = 10

by default, we do not write the 10   c = 4   and b = 10

log4 10 = log 12/log 4

log4 10 = log 12/ log 4

x+2 = log 12/ log 4

subtract 2 from each side

x +2 -2 = log 12/ log 4 -2

x = 1.79248125 -2

x =-.20752

not me

step-by-step explanation:

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