Question

ax^2+(1+a^2)x+1....xxx​

Answer 1

a²x² + (ax² + 1) x + a = (x + a) (ax² + 1)

Correct question: Factorize a²x² + (ax² + 1) x + a

∴ a²x² + (ax² + 1) x + a

= a²x² + ax³ + x + a

= ax³ + a²x² + x + a

= ax² (x + a) + 1 (x + a)

= (x + a) (ax² + 1)

This is the required factorization.

Another considered question:

Factorize ax² + (1 + a²) x + a

Solution:

Now, ax² + (1 + a²) x + a

= ax² + x + a²x + a

= ax² + a²x + x + a

= ax (x + a) + 1 (x + a)

= (x + a) (ax + 1)

This is the required factorization.

Similar problem can be read from here:

a²x² + (ax² + 1) x + a factorise by grouping method. - https://brainly.in/question/3072342

Answer 2

We have:

a$x^2$ + (1 + $a^2$) x + a

We have to find, the factorisation of a$x^2$ + (1 + $a^2$) x + a = ?

∴ a$x^2$ + (1 + $a^2$) x + a

= a$x^2$ + x + $a^2$x + a

= ax (x + a) + 1 (x + a)

= (x + a) (ax + 1)

∴ The required factorisation of a$x^2$ + (1 + $a^2$) x + a = (x + a) (ax + 1)

Thus, the required factorisation of a$x^2$ + (1 + $a^2$) x + a is equal to

"(x + a) (ax + 1)".