factors of 6 factors of 2 OI = add / sub Factor signs: 16 23 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 until you either find the correct combinationOR until 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 GCF Ex a. 6c 2 + 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 variable 2. Factor the first and last numeric term 3. 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 factor 4. 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.) 5p 2 22p + 8 No GCF factors 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)
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15 Factoring Trinomials Guess and Check :) · 2016-08-29 · (2c + 1)(3c + 2) 15 Factoring Trinomials Guess and Check :) & 4Term Polynomials Objective: To factor trinomials completely
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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.
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:
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.
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