Question 370439: How do u factor this trinomial 10a^2-9a+2 ?
Ex. 3x^2+10x+8
(4)(2)=8
(3x+4)(x+2)
(3x)(2)=6x
(4)(x)=4x
6x+4x=10x Answer by jsmallt9(3758) (Show Source):
You can put this solution on YOUR website!
With the 10 and 2 being positive and with the -9 in the middle, we can tell that the factors, if any, will both have minus signs, After all, we want products that are positive but a sum that is negative. So our factors will be of the form:
( - )( - )
(If you don't see this, then it will just take you longer to factor because you will be trying
( + )( + )
( - )( + )
( + )( - )
with no hope of any of these working.)
For the 10 in front we know that the factors are either 5 and 2 or 10 and 1. For the two in the back the only factors are 1 and 2. So the possibilities are:
(5a - 2)(2a - 1)
(5a - 1)(2a - 2)
(10a - 2)(a - 1)
(10a - 1)(a - 2)
The middle two:
(5a - 1)(2a - 2)
(10a - 2)(a - 1)
can't work because one of the factors has a common factor. Since does not have a common factor, we can't magically get one later. So we are now left with just:
(5a - 2)(2a - 1)
(10a - 1)(a - 2)
If you multiply these out, you will find that the first one works. So
(