User blog:Forestpaw13/Simplifying two Trinomials into Binomials.

Ooh... kay... now, since you guys did "so well" yesterday with the binomial thing, now I shall do trinomials back into binomials.

Ahem. Our problem is...

(x2 + 9x + 8).

First, we must look at the signs, or the pluses and minuses.  Notice how both signs are both pluses, so we don't really have to worry about anything.

So... we start with: (? + ?)(? +?)

Now. We take the square route of "x2".  Remember yesterday how I multiplied "x" times "x" and got x2? Well, today, we do the opposite.  You break x2 into "x" and "x", and put them into the problem.  (x + ?)(x + ?)

Next, we must figure out how to multiply to eight, and have the sum of the multiples add up to nine.

What are the multiples of eight, you ask?  1 • 8  2 • 4

Which two add up to nine? 2 and 4 add up to six, so it must be 1 and 8.  Put them in! It doesn't matter where they go! 

(x + 1)(x + 8)

Easy, eh?

What if I made it just a bit harder?

(2x2 + 8 + 6)

I won't go into the whole "x squared" thing, but notice how 2 is a prime number.

So...

(2x + ?)(x + ?) (There is an imaginary one, but anything times 1 equals itself, so... we'll leave it out.)

Okay, what times what equals six and adds up to eight?

Multiples of 6  1 • 6 2 •3

Uh-oh. None of those do.

Let me rephrase the question.  We already have - (2x + ?)(x +?)  You're going to have to multiply something by 2 to get to eight.

(2 • 6) + 1 = 13<BR> (2 • 1) + 6 = 8<BR> (2 • 2) + 3 = 7<BR> (2 • 3) + 2 = 8

There's two choices. <BR>

Your two possible answers are:


 * 1) (2x + 2)(x + 3)
 * 2) (2x + 6)(x + 1)

Do FOIL, they should both work out to the answer: (2x2 + 8 + 6)

Confusing much? There's so many different methods. If you want a different one, or you have any questions, just ask me. I'll be glad to help.

-- Geeky Forestpaw13 My Talk