Embed Size (px)
Citation preview
factors of 6 factors of 2OI = add / sub
Factor signs:1 62 3
1 2
(1+1)(6+2) = OI terms 6+2 = 8 (1+2)(6+1) = OI terms 1+12=13
(2+1)(3+2) = OI terms 4+3=7 (2+2)(3+1) = OI terms 2+6=8
+ +
You must try each factor combination untilyou either find the correct combination ORuntil you've tried them all and none will work. STOP when you find it!!!Remember the combination of the OI terms that ='s your middle term is the one you want!
Combo of OI terms:
No GCFEx
a. 6c2 + 7c + 2
Now the factored answer is: (2c + 1)(3c + 2)
15 Factoring Trinomials Guess and Check :)& 4Term Polynomials
Objective: To factor trinomials completely without the use of a calculator.
What to do with the signs:
+ + ( + )( + )
+ ( )( )
( + )( ) OR ( )( + )+ ( + )( ) OR ( )( + )
Steps:1. Check for a GCF
either # or variable2. Factor the first and last numeric term3. Make a chart of the OI terms (in FOIL)
you try different combinations until you find the one that matches the middle term in the original problem
***BE CAREFUL IF YOU HAVE A POS & NEG COMBINATION***Give the sign that matches the original middle term to the bigger multiple it will go in front of the correct back factor4. When you find the correct combination you put them inside the sets of ( ) as the factors. Be careful to place the correct sign with the right factor AND don't forget to split the variable in half.
b.) 5p2 22p + 8 No GCFfactors of 5: factors of 8:
1 5 1 8 signs: & combo 2 4
factor combinations(1 1) (5 8) OI terms = 1*8 1*5 = 8 5 = 13 NO(1 8) (5 1) OI terms = 1*1 8 *5 = 1 40 = 41 NO
(1 2) (5 4) OI terms = 1*4 2*5 = 4 10 = 14 NO(1 4) (5 2) OI terms = 1*2 4*5 = 2 20 = 22 YES
Now the factored answer is:(p 4)(5p 2)
c.) 6z2 5z 4No GCF
factors of 6: factors of 4:
1 6 1 4
2 3 signs: + & combo 2 2factor combinations
(1 1) (6 + 4) OI terms = 1*4 1*6 = 4 6 = 2 NO
(1 4) (6 + 1) OI terms = 1*1 4*6 = 1 24 = 23 NO
(1 2) (6 + 2) OI terms = 1*2 2*6 = 2 12 = 10 NO
(2 + 1) (3 4) OI terms = 2*4 1*3 = 8 + 3 = 5 YES
Now the factored answer is:
(2z + 1)(3z 4)
You have to think ahead about the signs since they are different. It WILL matter where you put them. Since the middle term is neg you need the bigger factor to have the neg sign.
d.) 20m5 + 13m3 21mGCF = m, so factor it out
20m5 + 13m3 21m m m m
20m4 + 13m2 21mfactors of 20: factors of 21:
1 20 1 212 10 3 74 5 signs: + &
factor combinations:(1 1)(20 + 21) OI = 1*21 + 1*20 = 21 20 = 1 NO(1 + 21)(20 1) OI = 1 + 420 = 419 NO(1 + 3)(20 7) OI = 7 + 60 = 53 NO(1 + 7)(20 3) OI = 3 + 140 = 137 NO(2 1)(10 + 21) OI = 42 10 = 32 NO(2 + 21)(10 1) OI = 2 + 210 = 208 NO(2 + 3)(10 7) OI = 14 + 30 = 16 NO(2 + 7)(10 3) OI = 6 + 70 = 64 NO(4 1)(5 + 21) OI = 84 5 = 79 NO(4 + 21)(5 1) OI = 4 + 105 = 101 NO(4 3)(5 + 7) OI = 28 15 = 13 YES
Now the factored form is:m(4m2 3)(5m2 + 7) don't forget to put your GCF in front
and split your variable in half!
One final tidbit: It's almost NEVER the factor that is 1 and itself, so try that factor combo last.
since the middle term is positive you need the bigger factor to get the +
e.) 15y12 y6 2
f.) 18x2 + 9xz + z2
l.) 30x2 123x + 63
To factor 4term polynomials:1. Check for GCF2. Group first two terms and last two terms together (put a plus between them)3. Factor out the GCF from each group. (If the leading term begins with a negative, factor the negative out and change the signs of the remaining terms)4. Compare the two sets of () if they are the same continue factoring, if they aren't stop and go back to step 2 and try regrouping the terms5. To continue factoring write the original GCF and then group the two new GCF's together and then include one of the remaining groups
EX GCF = 2x 3x(5x + 2) + 6(5x + 2) = 2x(3x + 6)(5x + 2)
EX.a. 3a2 2b 6a + ab b. 4x2 + v 2xv + 2x
c. x3 x2 + x 1 d. 10 + 2x 5z zx
e. 4x2 + 20x 3xy 15y f. 3x3 6x2 + 15x 30
g. x2 + ab ax bx h. x3 + 2x2 + 9x 18
