Step 5: Factoring trinomials by substitution
9x^4 + 45x^2 + 14.
Don't you think this expression would be easier to factor with smaller numbers and variable powers?
You can substitute a lower number and variable power like so:
Set n = 3x^2 (the GCF of the variable powers, and the square root of the GCF of the coefficients of numbers multiplied by a power of x). Then substitute it in by dividing the terms in the original expression by n.
n^2 + 15n + 14.
Now you can easily factor.
(n + 14) (n + 1).
Stick the 3x^2 back into the expression where the n's are.
(3x^2 + 14) (3x^2 + 1).