factor 3x^2 + 2x -1?

Question

I am not too sure on how to factor this. i thought maybe case 2 factoring but i don't remember how to do that so if someone could show me the steps for case 2 factoring or how to factor this polynomial that would be great.

Answer 1

Factors of 3x² are 3x and x:-
(3x----)(x----)
Factors of 1 are 1 and 1:-
(3x----1)(x-----1)
Now affix signs to obtain - 1 and + 2x:-
(3x - 1) (x + 1)

Answer 2

Do you know basic factoring? If not, add that under additional information and I'll revise this.

Alright, here's a trick for factoring when you've got a coefficient attached to the variable with the power. Look at the multiples of the coefficient, and the multiples of the last term.

For example, if you were trying to factor 3x^2 - 6x - 9, you'd want to look at the factors of four:
3 * 1

And the factors of 9:
3 * 3, or 9 * 1

You need to find the combination that will give you -8, and you only have so many possibilities. You also need to pay attention to the signs. Since 9 is negative, ONE of it's factors is going to be negative, too.

You can't use 9 * 1, because either your number will be too big (9 * 3), or too small (9 * 1) and (3 * 1) There is no way to make 8 out of 9 and 3.

So you'll have to use 3 * 1 and 3 * 3.

Since both the three and one will be multiplied by threes, all you need to worry about now are signs.

(3x-3)(x+3) is going to give you 3x^2 + 9x - 3x -9, or
3x^2 + 6x - 9. Since you need that 6 to be negative, you'll have to switch the signs so you'll be given a negative 9x.

So your solution must be (3x+3)(x-3).
Learn to go through possibilities in your head, it'll save you a good bit of time.


If that was too much for you, or badly explained, here's the short version:

You've got 3x^2 + 2x - 1

3, and 1 are the factors of 3. 1 and 1 are the factors of 1.
You've got a positive 2x and a negative 1, so you must have a positive 3x, since your only options are 3x and -x, or x and -3x. Only one of those combinations will give you 2x.

So you must have (3x-1)(x+1) because each term is being multiplied by each of the two terms in the opposite quantity.

Answer 3

There are two values for x they are
x1 = [ - 2 + ( (2^2) *- 4 * 3 * - 1) ^ 1/2 ] / 2 * 3
= [( -2+ (48) ^ 1/2] / 6

x1 = 0.821

x2 = [ -2 - ((2^2) * - 4 * 3 * - 1 ) ^ 1 / 2 ] / 2 * 3
= [(-2 - (48)^ 1/2 ] / 6

x2 =1.488

Answer 4

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

Answer 5

(x+1)(3x-1) pretty simple just use your brain and reverse thinking trial and error, or a TI-89.

Answer 6

(3x-1)(x+1)

Answer 7

(3x - 1) (x +1)

Answer 8

(3x-1)(x+1)