Question

✨ Please Provide Me With Solution.

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☑PROPER SOLUTION REQD.

Answer 1

Given Equation is p(x) = x^2018.

Given that it is divided by x^2 - 1.

= > x^2 - 1

= > x^2 - 1^2

We know that a^2 - b^2 = (a + b)(a - b).

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



Now,

We know that Dividend = Divisor * Quotient + Remainder.

                         x^2018 = Divisor * (x + 1)(x - 1) + ax + b

 
Substitute x = 1, we get

1^2018 = 0 + a(1) + b

1 = 0 + a + b

a + b = 1   ------------ (1)



Substitute x = -1, we get

(-1)^2018 = 0 + a(-1) + b

1 = -a + b

-a + b = 1    ------------- (2)

On solving (1) &(2), we get

a + b = 1

-a + b = 1

------------------

        2b = 2

           b = 1


Substitute b = 1 in (1), we get

a + b = 1

a + 1 = 1

a = 1 - 1

a = 0.


Remainder = ax + b

                   = 0 * x + 1

                   = 0 + 1

                   = 1.



Therefore:

|a| - |b| = |0| -|1|

            = -1.



Hope this helps!

Answer 2

Answer:

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