Thread: Polynomial factorization

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

I have to factorize this, but it seems almost impossible.Can anyone help? Preferably with the steps shown in proper order.

Originally Posted by Basal

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

I have to factorize this, but it seems almost impossible.Can anyone help? Preferably with the steps shown in proper order.

Perhaps you might show some steps? One approach is to expand, then show the form as Ax^2 + Bx + C. All quadratics can be written as the product of two factors, but not always with nice round numbers. It will not factor readily that I can see, so you might try using the quadratic formula if you must. Feasibility depends upon whether or not you allow radical quantities. Here's the form I am talking about:

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

I'll let you plug and chug.

Originally Posted by Diagonal

Perhaps you might show some steps? One approach is to expand, then show the form as Ax^2 + Bx + C. All quadratics can be written as the product of two factors, but not always with nice round numbers. It will not factor readily that I can see, so you might try using the quadratic formula if you must. Feasibility depends upon whether or not you allow radical quantities. Here's the form I am talking about:

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

I'll let you plug and chug.

Already tried.It goes like this :-

(a^2 +1)x^2 - [(a^2 + 1)^2 - 1]x + (a^2 + 1)

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

=x(a^2 + 1)[x -(a^2 +1)] + 1 [x + (a^2 + 1)]

Ideally, I'd take a common factor at this point, but there is none.This is my problem.