How do you factor in algebra?

Answer 1

factoring in algebraFollowing is one of the examples of solved algebra problems.

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