Question

what is the hcf of (x²+bx-x-b) and x²+x(a-1)-a​

Answer 1

Answer:

Let us first factorize the given polynomials x

2

+bx−x−b and x

2

+x(a−1)−a as shown below:

x

2

+bx−x−b=x(x+b)−1(x+b)=(x−1)(x+b)

x

2

+x(a−1)−a=x

2

+ax−x−a=x(x+a)−1(x+a)=(x−1)(x+a)

We know that the highest Common Factor (H.C.F) of two (or more) numbers is the largest number that divides evenly into both numbers.

Now, from the above factorization, we get that (x−1) is the common factor.

Hence, the HCF of x

2

+bx−x−b and x

2

+x(a−1)−a is x−1.

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Answer 2

Answer:

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