Question

Factorize:
a²x²+(ax²+1)x+a

Answer 1

Answer:

a^2x^2 + ax^3 + x + a

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

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

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

=> x = -a, (√-1)/a, (-√-1)/a

_____________

Answer 2

Concept :  

Factorisation by regrouping the terms :  

Sometimes it is impossible to find out a common factor from all the terms of a given expression. So we group the terms to have a common factor.  Then common factors are taken from each group.

Given : a²x² + (ax² + 1)x + a

= a²x² + a + (ax² + 1)x

= a(ax² + 1) + x(ax² + 1)

= (ax² + 1) (a + x)

Hence, the factorisation of a²x² + (ax² + 1)x + a is (ax² + 1) (a + x).

HOPE THIS ANSWER WILL HELP YOU…..

 

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