SOLUTION: Is 7x^2 - 12x + 6 prime or can it be factored?

Question 335490: Is 7x^2 - 12x + 6 prime or can it be factored?
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 :
1,2,3,6,7,14,21,42
-1,-2,-3,-6,-7,-14,-21,-42

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

These factors pair up and multiply to .
1*42 = 42
2*21 = 42
3*14 = 42
6*7 = 42
(-1)*(-42) = 42
(-2)*(-21) = 42
(-3)*(-14) = 42
(-6)*(-7) = 42

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	42	1+42=43
2	21	2+21=23
3	14	3+14=17
6	7	6+7=13
-1	-42	-1+(-42)=-43
-2	-21	-2+(-21)=-23
-3	-14	-3+(-14)=-17
-6	-7	-6+(-7)=-13

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
Is this polynomial prime, {{{2m^2+11mn+9n^2}}}, or can it be factored out... (answered by jim_thompson5910)

can this be factored or is it prime? 2a^2... (answered by MathLover1)

49x^2+56x+16 Can this equation be factored or is it prime Can someone solve and show me... (answered by ankor@dixie-net.com)

Determine whether or not if it can be factored. If not, then state it is prime. 3x^2 +... (answered by jim_thompson5910)

Determine whether or not if it can be factored. If not, then state it is prime. 2x^2 +... (answered by jim_thompson5910)

Determine whether or not if it can be factored. If not, then state it is prime. 3x^2 +... (answered by checkley77)

factor, if the polynomial cant be factored then it is prime x^2+7x+10 please show... (answered by MathLover1)

factor the polynomial if it cant be factored it is prime 8x^5+16x^4-20x^3+12 please (answered by Edwin McCravy)

what is the simplified form of (2b-3c)^3? and is (X^2)-7x+5 consider prime ,becuse it... (answered by stanbon)