## 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).