[perhaps]

Factoring Trinomials


Example #1:

(x + 2) (x + 3)
= x^2 + 3x + 2x + 6
= x^2 + 5x + 6

Note --> For the previous answer, the coefficent +5 is the sum of +3 and +2 and the coefficient +6 is the product of +2 and +3.


Example #2:

Question: x^2 - 6x + 8

From this we can see that:
*The SUM (middle number ) is -6 and that
*The PRODUCT (last number ) is +8
So the intergers have to be two numbers that when added together, create the sum of "-6" and when multiplied together, create the product of "+8"
From this bit of information we can come to the conclusion that the integers would be -2 and -4

So now we have to complete the question by "inserting" the correct integers into the brackets, while keeping the same variable (oh gosh, I hope "variable" is the correct word LOL...by "variable" I mean "x" in this particular question ). Here is the full solution:

Question: x^2 - 6x + 8
Answer: = (x - 2) (x - 4)


Example #3:

Question: y^2 - 2xz - 48z^2
Sum: -2
Product: -48
Integers: -8, +6
Answer: = (y - 8z) (y + 6z)


Example #4:

2x^2 + 6x - 20
= 2 (x^2 + 3x - 10) [note ---> see how I pulled out the GCF (2) first]
= 2 (x - 2) (x + 5)


Factoring Checklist:
1. Look for GCF
2. Factor trinomials

[perhaps]

Factoring A Difference Of Squares

Always has to be a difference (aka. Subtraction) of squares!

(x + y) (x - y)
= x^2 - xy + xy - y^2
= x^2 - y^2

The factored form of x^2 - y^2 = (x + y) (x - y).

(It's hard to explain this so just follow the pattern )


Example #1:

36x^2 - 49
= (6x + 7) (6x - 7)


Example #2:

16m^2 - 121n^2
= (4m + 11n) (4m - 11n)


Example #3:

3a^3 - 12ab^2
= 3a(a^2 - 4b^2)
= 3a(a + 2b) (a - 2b)


Example #4:

81a^4 - 16
= (9a^2 - 4) (9a^2 + 4)
= (3a - 2) (3a + 2) (9a^2 + 4)


**Look for GCF's first!
**Make sure you factor FULLY!


Example #5:

(x + 3)^2 - y^2
= [(x + y) + y] [(x + 3) - y]
= (x + y + 3) (x - y + 3)

NOTE: Notice how I emphasized the "-" in the answer since it was multiplied by a negative variable and as the rule says --> A negative and a positive equal a negative.

**The square terms may not be monomials.


Let me know if this helps or if you need more complicated/simpler stuff.

[Jay42]

Originally posted by perhaps
this is like when i found out the saying was "Play it by ear" instead of "play it by year"

Now that would take talent!
"Gimme some Pink Floyd The Wall, circa 1981. That last time you played it just sounded like SO 1980."

[perhaps]

LOL! No see, I thought it meant "play it by year" like 'take it as the day goes by' ...live the day out and see how things go, instead of planning ahead.

See? It sorta makes sense...