3x²+5x-2 How do I factor this trinomial?

Question

Please give me a good explanation I am having the hardest time learing this. I know it's not really that hard but some problems just stump me

Answer 1

Well the answer is (3x-1)(x+2).  You can use the FOIL method to make sure that this is the factor of the trinomial.  If I'm not mistaken, Foil stands for Front, Outside, Inside, and Last.  For (3x-1)(x+2), you first do the front by multiplying.  (3x)(x) = 3x^2, then the outside with (3x)(2) = 6x, Inside (-1)(x)=-x, and last the outside (-1)(2) = -2.  So you would have 3x^2 + 6x -x -2 = 3x^2 + 5x -2!

Normally, I would first figure out the possibilities of getting 3x^2 first and then possibilities for -2 and when I put them together I use the foil method and see what becomes the answer.  I hope this helps.

Answer 2

(x + 2)(3x - 1)

one way to do this when a <> 1 is to factor by grouping...

look at the first and last coefficients: 3 and -2, and find their product: -6

now look for factors of -6 that can be summed to give the middle coefficient +5

-6 = (6 * -1), and 6 - 1 = 5... that looks like it

now break 5x into 6x - x

3x^2 + 6x - x - 2

factor in pairs:

3x(x + 2) - 1(x + 2)

factor out the (x + 2)

(x + 2)(3x - 1)

factoring by grouping is a useful tool for factoring trinomials where a doesn't = 1

Edit:

3x^2 + 6x - x - 2

looking at the last two terms: what's the greatest common factor?  looks like 1

this would give us: 3x(x + 2) + 1(-x - 2)

but this isn't what we need, we need to change signs of both terms in the parenthesis; therefore, instead of

3x(x +2) + 1(-x - 2), we factor out the negative from each and make it 3x(x +2) - 1(x + 2)... that gives a common factor to take out of each term now (mainly x + 2)

Answer 3

3x^2+5x-2                    

3x^2+6x-1x-2

3x(x+2)-1(x+2)

(3x-1)(x+2)

(ok first get two numbers which when multiplied give you -6 (product of the first and the third term) and when added give you the middle term i.e +5x. Those two numbers then would be +6x-1x. Their product gives us -6 and their sum gives us 5x. Thus, they would be put in the place of the middle term. The rest would remain the same. After that the answer is pretty much self explanatory.)