Question

the hcf of x^3+1 and x^4-1 is​

Answer 1

Solution:-

The factors of (X^3 + 1) = (X + 1) (X^2 + 1^2 + 2 X)

The factors of (X^4 – 1) = (X^2 – 1) (X^2 + 1)

= (X + 1) (X – 1) (X^2 + 1)

Then, the H. C. F. of X^3 + 1 and X^4 – 1 = X + 1

Answer 2

The hcf of $x^{3} + 1$ and $x^{4} -1$ is​ $(x+1)$.

Step-by-step explanation:

Given:

$x^{3} + 1$

$x^{4} -1$

To Find:  

The hcf of $x^{3} + 1$ and $x^{4} -1$.

Solution:

As given,$x^{3} + 1$.

Factorizing $x^{3} + 1=(x+1) (x^{2} -x+1),$

                                              Using identity $p^{3} +q^{3} =(p+q)(p^{2} -pq+q^{2} )$.

Factorizing $x^{4} -1=(x^{2} -1)(x^{2} +1)$

                              $=(x-1)(x+1)(x^{2} +1)$,

                                               Using identity $(p^{2} -q^{2} )=(p-q)(p+q)$.

Therefore,The hcf of $x^{3} + 1$ and $x^{4} -1$  $=(x+1)$.

Thus,the hcf of $x^{3} + 1$ and $x^{4} -1$  is  $(x+1)$.

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