Factorise: 2x^2-3x+1?

Question

Can you explain how you get it?
Im confused :/

Answer 1

Connie's answer is correct. The factors are (2x - 1)(x - 1).

To get the answer requires a little bit of intuition. You start by factoring the first term, which is 2x^2. This can be factored into 2x and x. (It can also be factored in 4x and x/2, and a lot of other combinations, but these are unlikely.) So we know the factors are probably of the form

(2x )(x )

Now we look at the last term which is 1. The factors for 1 are either +1 and +1, or -1 and -1. Noticing that the middle term, -3x, is negative, we try -1 and -1 for the factors of 1. Putting them into the parentheses above, we get

(2x - 1)(x - 1)

Now we multiply this out to see if we get the original problem.

2x^2 - x - 2x +1

or, 2x^2 - 3x +1

If we didn't get the correct product, then we would have to try other factors. After you've done a number of these problems it becomes easy.

Answer 2

Okay, so you have 2x^2 – 3x + 1…
The end result is going to have two sets of these: (..)(..)
What two numbers (multiplied) will equal 2x^2?
The answer is 2x and x.
So, you put the 2x in one bracket and the x in the other...
(2x..)(x..)
So now, you have to think, what two numbers can you multiply to equal 1, but add to equal -3? It would be -1 and -1. This sounds confusing because you think, " -1 + -1 = -2".
This is true, but you have to put the -1's in the brackets before multiplying: (2x-1)(x-1). To double check, do this: (multiply)
2x (x) + 2x(-1) + -1(x) +-1(-1)
2x^2 - 2x -x +1
2x^2 -3x +1

Do you notice how the first and last numbers multiplied (2x and -1), plus the two middle numbers multiplied (-1 and x), added together, equal the ?x value? When you are looking for the two numbers at the beginning, use these numbers to help you in you factoring.

P.S. (2x-1)(x-1) is the final result in factoring UNLESS the equation is set equal to zero. Then, 2x-1=0 and x-1=0
You have to solve, so x=1/2 and x=1. Since you're just factoring, then the correct answer is the one in bracket : )
Hope this helps!!!

Answer 3

(2x-1)(x-1)
x = 1/2
x = 1