Question

Hello friends!!!!!!

Factorisation by grouping method

Solve my questions which are attached.

Answer should contains...

Steps wise
Clear concept
Aqurate answer

Answer 1

52.

Given Equation is x^3 - x^2 + ax + x - a - 1

= > x^3 - x^2 + ax - a + x - 1

Step 1: Factorize each group

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

Step 2: Now take out the common factor.

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





53.

Given f(x) = x^3 + x^2 - x - 1

                 = (x^3 + x^2) + (-x - 1)

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

 Factor x^2 - 1 = (x + 1)(x - 1)

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

                 = (x + 1)^2(x - 1)




Given g(x) = x^3 - x^2 + x - 1

                  = (x^3 - x^2) + (x - 1)

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

                  = (x - 1)(x^2 + 1)


Now,

p(x) = f(x) * g(x)

       = (x + 1)^2(x - 1) * (x - 1)(x^2 + 1)

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




Hope this helps!