Factoring in math. .Solve problem: 2x^2-x-1?

Answer 1

(2x + 1) (x - 1)

Answer 2

1

Answer 3

This is a farely simple polynomial to factor. First recognize that all of the coefficients are prime: 2, -1, and -1. I like to start by creating parenthesis: ( )( ). Then I start adding the first numbers in each set of parenthesis. So how can we split 2x^2 into two terms? How about: 2x * x or (2x^2) * 1 or 2 * x^2
Well, when foiling back out our factor we will need an x in the second term so we need to split the x's up. So I choose 2x * x
So let's put what we have in our parenthesis: (2x )(x ). That's half the battle. So now we can recognize that there are two negatives in the original statement. We know that we must multiply a negative and a positive to get a negative so we will have either (2x-?)(x+?) or (2x+)(x-?). OK, now we almost got it. So let's look at our last term in our original statement: -1. What can we multiply together to get -1? 1 and -1 are the only integers I can recall. Now if we look at our two possible solutions, we remember that we already have the signs worked out so we get a negative. So all we need to do is plug in 1 and 1.So let's simply plug those two numbers into both of the possible solutions we came up with:
(2x-1)(x+1) and (2x+1)(x-1). Great! Now let's just foil these back out to see which gives us our original statement:
(2x-1)(x+1) = (2x^2)+2x-x-1=(2x^2)+x-1 That's not what we want so let's try the other: (2x+1)(x-1) = (2x^2)-2x+x-1=(2x^2)-x-1. Now that's what we want. So the answer is (2x+1)(x-1). But we don't have to stop there. We can solve for x by setting each parenthesis set equal to 0. 2x+1= 0 and we get x=-1/2 and x-1=0 and we get x=1. Hope this helps

Answer 4

First: multiply the 1st & 3rd term to get -2. Find two numbers that give you -2 when multiplied & -1 (3rd term) when added/subtracted. The new middle numbers are (1 & -2).

Sec: place the new middle numbers in the expression.

2x^2 +1x - 2x - 1

Third: group "like" terms & factor both sets of parenthesis.

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

Third: combine the inner term (once) with the outer term.

(2x + 1)(x - 1) or, (x - 1)(2x + 1)

Answer 5

2x^2 - x - 1
= (2x + 1)(x - 1)
x = -1/2 or x = 1

Answer 6

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

Answer 7

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

Answer 8

(2x + 1)(x - 1)

x = -1/2 or x = 1

Answer 9

(2x + 1)(x - 1)

look at the end.
- 1... 2 numbers multiplied together = 1
that can only be 1 and 1
now since it's negative, one has to be positive and the other negative
plug in from there and you got it

Answer 10

(2x + 1)(x - 1)