Algebra Honors ( Periods 4 & 7)

CHAPTER 8-5: (2nd part that we skipped) FACTORING 4-TERM POLYNOMIALS

It’s always been called FACTORING BY GROUPING before the Common Core ;)

Today, you'll have 4 TERMS IN YOUR POLYNOMIAL!
You put the polynomial in 2 sets of 2 by using ( )s
Then you factor out the GCF for each set of 2 terms

DOES THIS ALWAYS WORK FOR EVERY 4 TERM POLYNOMIAL?
Of course not! But for this section of the math book, it will!

What happens if it doesn't work? The polynomial may just not be factorable! (prime)

MAKE SURE IT'S IN DESCENDING ORDER FIRST!!!!

EXAMPLE: 6x³ - 9x² + 4x - 6

NOTICE THAT THERE IS NO GCF OF ALL 4 TERMS!

Factoring by grouping says if there is no GCF of all 4 terms, look and see if there is a GCF of just 2 terms at a time.

Put ( ) around the first 2 terms and the 2nd 2 terms:
(6x³ - 9x² ) + (4x - 6)

Always make sure that there is a + sign in between the two pairs of (   ). If there is a negative sign in front of the 3rd term, keep it inside the 2nd set of (  ) and add a + sign in between.

FACTOR OUT THE GCF FROM EACH SET OF TWO TERMS:
3x² (2x - 3) + 2(2x - 3)

        LOOK AND SEE IF WHAT'S LEFTOVER IN THE (  ) IS THE SAME:

In this case, it was because they were both (2x - 3)

So now this is a GCF of both terms and you can factor that out:
(2x - 3)(3x² + 2)

ALWAYS MAKE SURE THAT IF THERE IS A NEGATIVE ON THE THIRD TERM, PLACE IT IN THE SECOND (  ) AND ALWAYS HAVE A + BETWEEN THE TWO SETS OF (  )

Always ask " Am I done" to MAKE SURE YOU CAN'T FACTOR ANY MORE!

HOMEWORK: