Question

Factorise x^
3+2x^2+2x+4​

Answer 1

Answer:

There are many methods of finding a real root and factorisation. But for this sum we can use an easy method called the ‘ Trial and error method’

We notice that if we put ‘x’=2; the above polynomial expression(x^3-2x-4) results in ;

(2)^3-(2×2)-4= 8-4-4= 0

So; (x-2) can be taken as a factor of the given expression.

So, x^3-2x-4

=x^3-2x^2+2x^2-4x+2x-4

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

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

[ note that (x^2+2x+2) cannot be further factorised into real factors as the roots come as complex by Sreedhar Acharyas rule of finding roots.)

So; the required factorisation is ;

x^3-2x-4=(x-2)(x^2+2x+2)