Step 5: Factoring trinomials by substitution

Picture of 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).
sandyr19503 years ago
These things that are being factored are not EQUATIONS as stated in the text because they do not contain equal signs. They are called EXPRESSIONS. This is important because different things can be done with equations (such as solving) than can be done with expressions.
Phoenixsong (author)  sandyr19503 years ago
Will fix, thanks.
mi9d6 years ago
Sorry, but shouldn't n=3.x.x ?
I mean 9.x.x times 9.x.x = 81.x.x.x.x

( sorry, can't type the power superscripts )
Mattonator mi9d6 years ago
9x2 times 9x2 is 81 * 81 which = 6561 which is the same as 9*9*9*9 or 94.

814 is 43,046,721
Phoenixsong (author)  mi9d6 years ago
Oh, and btw, to type power superscripts, put a carrot (shift+6) both in front of and in back of the number/word/phrase that you want in superscripts.
Phoenixsong (author)  mi9d6 years ago
Gotcha. Thanks for catching that.