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Suppose you have the problem:
x2 +6x+9
you try to find two numbers that add to be 6 and multiply to be 9. in this case it's 3 and 3. so you exchange the 6x for 3x +3x . . .
x2 +3x +3x +9 then you group the first two and the second two terms . . .
(x2+3x)+ (3x+9)
next you take out the biggest number they have in common.and leave whats left in the ( )
x(x+3)+ 3(x+3)
now the answer is the stuff inside the ( ) times the stuff outside
(x+3)(x+3)
more stuff . . .
The example given above is known as factoring a trinomial into two binomials.
Not all trinomials are factorable. The general form of a trinomial is:
ax2 + bx + c
If the trinomial is indeed factorable, there must exist two factors for the product of the coefficients a and c, a x c, that will add together to equal the coefficient b.
The signs of the coefficients are critical:
If ac is positive, both factors are either negative or positive
If ac is negative, only one of the two factors can be negative
If b is negative, at least one of the two factors must be negative
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