SOLUTION: Help explain why this expression cannot be factored 40a^2+21a-2

Question 681794: Help explain why this expression cannot be factored
40a^2+21a-2
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 :
1,2,4,5,8,10,16,20,40,80
-1,-2,-4,-5,-8,-10,-16,-20,-40,-80

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

These factors pair up and multiply to .
1*(-80) = -80
2*(-40) = -80
4*(-20) = -80
5*(-16) = -80
8*(-10) = -80
(-1)*(80) = -80
(-2)*(40) = -80
(-4)*(20) = -80
(-5)*(16) = -80
(-8)*(10) = -80

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	-80	1+(-80)=-79
2	-40	2+(-40)=-38
4	-20	4+(-20)=-16
5	-16	5+(-16)=-11
8	-10	8+(-10)=-2
-1	80	-1+80=79
-2	40	-2+40=38
-4	20	-4+20=16
-5	16	-5+16=11
-8	10	-8+10=2

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
Explain why a^2+b^2 cannot be... (answered by solver91311)

explain why a^2 + b^2 cannot be a... (answered by Mathtut,solver91311)

how is this problem factored?... (answered by Earlsdon)

can you please help me solve this: Factor each expression. If the expression is in... (answered by 303795)

can you please help me solve this? Identify the excluded values for each expression... (answered by Earlsdon)

Hello out there,I need some help with some problems,the first one is,Factor.Write prime... (answered by stanbon)

why can't this be factored... (answered by jim_thompson5910)

the expression 2x+5/4 cannot be simplified (i.e. the 2 and the 4 do not reduce). explain... (answered by jim_thompson5910)