Factor Polynomials

Question

Factor

9x^10+12x^5+4

Answer 1

Notice that the powers of the x terms are multiples of 5.

 

So do a substitution to make it easier.  Let y = x⁵.

 

So the polynomial becomes 9y² + 12y + 4

 

Now factor this as (3y + 2) (3y + 2) = (3y + 2)²

 

Now substitute x⁵ back in for y and you get:  (3x⁵ + 2)²