Question

39. If the divisor,quotient and remainder are (x + 1),(x - 1) and 1 respectively, then the dividend is​

Answer 1

Answer:

(x+1)(x-1) +1

x^2-1+1

x^2

Answer 2

Step-by-step explanation:

Given :-

The divisor,quotient and remainder are (x + 1),

(x - 1) and 1 respectively.

To find:-

Find the ddividend ?

Solution :-

Given that

The divisor = (x+1)

The quotient = (x-1)

The remainder = 1

We know that

Division Rule :-

Dividend = Divisor×Quotient+Remainder

On Substituting these values in the above formula then

=> Dividend = (x+1)(×(x-1)+1

=> Dividend = (x^2-1^2)+1

Since (a+b)(a-b)=a^2-b^2

=> Dividend = x^2-1+1

=> Dividend = x^2+0

=> Dividend = x^2

Answer:-

The dividend for the given problem is x^2

Alternative Method :-

By Euclid's Division Lemma

a = bq+r

=> a = (x+1)(x-1)+1

=> a = x^2-1+1

=> a = x^2

Dividend = x^2

Used formulae:-

Division Rule :-

Dividend = Divisor×Quotient+Remainder

• (a+b)(a-b)=a^2-b^2

Euclid's Division Lemma:

For any two Positive integers a and b there exist two Positive integers q and r satisfying a= bq+r , 0≤r<b.