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caylus
Hello,

x^4-1=(x²-1)(x²+1)=(x²+1)(x-1)(x+1)
==>(x^4-1)/(x-1)=(x²+1)(x+1)=x^3+x^2+x+1
Answer C

Answer:

Option C.

Step-by-step explanation:

We have to solve [tex]\frac{x^{4}-1 }{x-1}[/tex] by synthetic division and tell the quotient.

First we will write the numerator in the standard form as [tex]ax^{4}+bx^{3}+cx^{2}+dx+e[/tex]

Which will become as [tex]1.x^{4}+0.x^{3}+0.x^{2}+0.x^{1}-1[/tex]

Since denominator of the fraction is (x -1) therefore we take x = 1 as zero root.

Now we form the synthetic form as below

          1        0      0    0      -1

1          1        1       1      1      0

          x³      x²      x    

Here coefficient of x³ is 1, for x² is 1, for x is 1, and constant term 1.

Now the fraction will come in the form of  

[tex](x -1) + \frac{(1.x^{3}+1.x^{2}+1.x+1)}{(x - 1)}[/tex]

Therefore quotient will be [tex]x^{3}+x^{2}+x+1[/tex]

Option C. is the answer

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