Question

find the HCF of x^4 -1 and x^3+ x^2+ x + 1

Answer 1

Answer:

Step-by-step explanation:

Answer 2

The HCF of $x^4-1$ and $x^3+ x^2+ x + 1$ is $(x^2+1)(x+1)$

Explanation:

The given expressions are : $x^4-1$ and $x^3+ x^2+ x + 1$

First factorize each expression :

$x^4-1= x^2-1^2\\\\=(x^2+1)(x^2-1)\\\\=(x^2+1)(x+1)(x-1)$

[∵ $a^2-b^2=(a+b)(a-b)$]

So , factors of $x^4-1$  are $1 ,\ (x^2+1)\ ,\ (x+1)\ , (x-1),\ \ (x^2+1)(x+1),\ (x+1)(x-1),\ (x^2+1)(x-1),\ (x^2+1)(x+1)(x-1)$

In second expression :

$x^3+ x^2+ x + 1= x^2(x+1)+x+1\\\\=(x+1)(x^2+1)$

[Taking (x+1) out as common.]

So , factors of $x^3+ x^2+ x + 1$ are $1,\ (x+1),\ (x^2+1),\ (x+1)(x^2+1)$.

HCF = Highest common factor.

Now , we can see that the highest common factor from both expressions is $(x^2+1)(x+1)$

Hence, the HCF of $x^4-1$ and $x^3+ x^2+ x + 1$ is $(x^2+1)(x+1)$

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The HCF of (x - 3)2 (x + 4)2 and (x - 1) (x + 4) (x - 3)2 is

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