## Step 5: Factoring trinomials by substitution

^{^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).

I mean 9.x.x times 9.x.x = 81.x.x.x.x

( sorry, can't type the power superscripts )

^{2}times 9x^{2}is 81 * 81 which = 6561 which is the same as 9*9*9*9 or 9^{4}.81

^{4}is 43,046,721