2. FACTORING An ALGEBRAIC Adventure FACTORING An ALGEBRAIC Adventure Don’t be a scaredy CAT

3. Factoring-a way of life in MATH Begin the journey for success in FACTORING Go for it…

4. How do you factor a Monomial term. Always check for a common factor. Check all NUMBERS first and then all Check all NUMBERS first and then all VARIABLES. VARIABLES. 8X 3 + 2X 2 – 10X 8X 3 + 2X 2 – 10X The common NUMBER (Factor) is 2 The common VARIABLE (Factor) is X Divide each term by 2X So……. 2X(4X 2 + X – 5) is the factored form.

5. Remember: To factor you look for a common number and/or variable to “divide” out of each “term”. 4X 5 + 8X 4 – 12X 3 + 16X 2 4X 5 + 8X 4 – 12X 3 + 16X 2 There are FOUR “terms” in this algebraic expression. A “term” is separated by a “+” or “-” sign. 4 is the “common” numeric factor and the largest power the variables have in “common” is a “2”. So, let’s “divide” by 4 and subtract 2 from each exponent of “X”. 4X 2 ( X 3 + 2X 2 – 3X 1 + 4) 4X 2 ( X 3 + 2X 2 – 3X 1 + 4)

6. Factoring Monomial terms #1. X 2 + 2X Answer: X(X + 2) Divided by “X” #2. 4Y 3 - 12Y 2 Answer: 4Y 2 (Y – 3) Divided by “4Y 2” #3. 12W 4 + 9W 2 – 6W Answer: 3W(4W 3 + 3W -2) Divided by “3W” (Remember to SUBTRACT Powers when dividing Variables) Click speaker for sound

7. Now try these: (Factor) 1. 10X 2 -5X 2. 13Y 3 +26Y 2 -39Y Click to See Answer (Y 2 + 2Y - 3) 3. 16U 4 - 28U 3 + 4U 2 (2X – 1) 13Y 5X Click to See Answer 4U 2 (4U 2 -7U+1)

8. Let’s try some more: 1. 100Y 5 – 50Y 4 + 25Y 3 Click to See Answer 25Y 3 ( 4Y 2 – 2Y + 1) 2. 16M 2 + 32M 3 – 40M 5 Click to See Answer 8M 2 ( 2 + 4M – 5M 3 )

9. Factoring TRINOMIALS (3) First, let’s multiply two “binomials” (2 terms) (X + 4)(X + 6)= X 2 + 10X + 24 How does this work? “FOIL”-  First Outer Inner Last (FO + IL)(FI+ OL) So, follow the steps: F’s multiplied, then O’s next, then I’s, then finally, L’s, then simplify all terms……. simplify all terms…….

10. Now try to multiply these Binomials: (X – 6)(X + 8) X 2 + 2X - 48 (X – 7)(X – 4) X 2 – 11X + 28 Click to See Answer

11. How to Factor TRINOMIALS?? X 2 + 10X + 24 X 2 + 10X + 24 First, look at the sign of the last term, in this case it’s positive (+). Next, look at the sign of the middle term, in this case a positive (+), SO both signs in your factors will be positive (+). Now, find ALL factors of the last term (24). 1 * 24; 2 * 12; 3 * 8; 4 * 6----now, since the last term has a + in front of it, which factors will ADD up to the middle term of 10.

12. So, now we have: (X + 6) (X + 4) Now let’s factor: X 2 + 2X – 48 X 2 + 2X – 48 Now we must look again at the sign of the last term ( - ). It is negative, so the factors of 48 now must subtract to render a + 2 in the middle term: 1 * 48; 2 * 24; 3 * 16; 4 * 12; 6 * 8----the factors that multiply to give 48 and subtract to give us a 2 are 6 and 8. The larger factor, in this case 8, will get the + and the 6 will get the -. SO: (X + 8)(X – 6)

13. Now YOU try Factoring TRInomials Click to See Answer