SOLUTION: How do you factor x*x +6x+12 ?

Question 783438: How do you factor x*x +6x+12 ?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Looking at the expression , we can see that the first coefficient is , the second coefficient is , and the last term is .

Now multiply the first coefficient by the last term to get .

Now the question is: what two whole numbers multiply to (the previous product) and add to the second coefficient ?

To find these two numbers, we need to list all of the factors of (the previous product).

Factors of :
1,2,3,4,6,12
-1,-2,-3,-4,-6,-12

Note: list the negative of each factor. This will allow us to find all possible combinations.

These factors pair up and multiply to .
1*12 = 12
2*6 = 12
3*4 = 12
(-1)*(-12) = 12
(-2)*(-6) = 12
(-3)*(-4) = 12

Now let's add up each pair of factors to see if one pair adds to the middle coefficient :

First Number	Second Number	Sum
1	12	1+12=13
2	6	2+6=8
3	4	3+4=7
-1	-12	-1+(-12)=-13
-2	-6	-2+(-6)=-8
-3	-4	-3+(-4)=-7

From the table, we can see that there are no pairs of numbers which add to . So cannot be factored.

===============================================================

Answer:

So doesn't factor at all (over the rational numbers).

So is prime.

RELATED QUESTIONS
how do you factor x^2... (answered by rfer)

How do you factor 6x^2+x-12=0. Could you please help... (answered by jim_thompson5910)

how do you factor... (answered by richwmiller)

How do you factor 6x^2+x-2? (answered by richwmiller)

How do you factor 6x squared minus x minus 15 (answered by lynnlo,MathTherapy)

How do you factor 3x^3 + 6x^2 + x +... (answered by FrankM)

How do you factor out x^3-x^2-6x? HELP... (answered by Alan3354)

How do you factor this expression:... (answered by ankita_vashishtha@yahoo.co.in)

How do you factor this polynomial... (answered by edjones)