Question

how do you factor 2x^2 -7x +6 ?
how do you factor 2x-3, if possible?
how do you factor 2x^2+5x-3?
can you factor 2x-1? If yes how?

Answer 1

yes i know that but i want the answers after they have been factored

Answer 2

2x-3 and 2x-1 do not (really) factor. Suppose you would put a two in front of the brackets: 2x-1 = 2(x-½). Not a good way to factor, because of the fraction.

Answer 3

Now for 2x^2-7x+6.
If you are lazy think of it as solving the equation 2x^2-7x+6=0 with the abc-formula:
Then\[x=\frac{ 7\pm \sqrt{49-48} }{ 4 }=\frac{ 7 }{ 4 }\pm \frac{ 1 }{ 4 }\]So x = 2 or x = 1½.
How does this relate to 2x^2-7x+6?
Suppose you are not lazy ;) and you don't do everything with the abc formula, but by factoring as much as possible.

You could factor it as follows:\[2x^2-7x+6=(2x-3)(x-2)\]

Answer 4

wait what about how do you factor 2x^2+5x-3?

Answer 5

@Hero: I go along with that! Mostly I am only lazy when the coefficient of x² <>1, because everything becomes just a little more complicated then...

Answer 6

waot @ZeHanz can you answer the other question in this problem :(

Answer 7

@Hero: it means: the coefficient of ax^2, a ≠1
Let's try it the "right" way:
\[2x^2+5x-3=(2x....)(x....)\]

Answer 8

this is way better than yahoo answers :) js
thank you @ZeHanz

Answer 9

(2x-1)(x+4) ?

Answer 10

or x-4

Answer 11

Well, I'm trying not to be ZeHanz answers ;) I explain and leave something to do for you!

(2x....)(x....) is not so difficult to see: after all, 2x*x = 2x².
Think about the FOIL-process: the product of the Last number must be -3. Also they must be "nice" numbers, otherwise they wouldn'd let you do this stuff...

Answer 12

yeah but -3 and -1 do not equal 5?

Answer 13

is it -2 then? IDK

Answer 14

Hero leave.

Answer 15

idk what 2 numbers add to -3 and multiply to 5

Answer 16

The do not need to be. That's why this is more complicated: the 2 before x² plays a role as well. If you think of it, the numbers can only be -1 and 3 or 1 and -3, because of product -3. That gives us 2 possibilities:

1. (2x-1)(x+3)=2x²+6x-1x-3=2x²+5x-3 <<< this is right!
2. (2x+1)(x-3)=2x²-6x+1x-3=2x²-5x-3

Answer 17

oooooooh okay! got it thank you

Answer 18

YW!

Answer 19

can you look at the message i sent you, including a problem that i can not ask for 8 minutes. i just need the first step and i think i can figure it out from there

Answer 20

@Hero: there is a misunderstanding: I only meant to say (and I did, just re-read) that if the coefficient of x^2 is not equal to 1, factoring becomes more difficult.

Answer 21

@Hero: I know, I responded to your not understanding my use of notation.
I thought it was generally known that ≠ and <> stand for the same thing.

Answer 22

I guess <> is more a programmer's thing ;)

Answer 23

No, it's programmer's notation, because ≠ is not on most keyboards.
It surprises me tha WA is not clever enough to know it ;)

Answer 24

I'm sorry I offended you, but I think you are being too harsh on me.

What about the widely used x^2. One could easily argue that ^ is also programmer's notation, precisely because of the same keyboard issue.
That's why we can use LaTeX.

If you read the answers I've given lately, you will see that very often I rewrite the (sometimes very poorly written formulas) in the equation editor, for the very reason you criticise me: to use better notation.

Answer 25

Speak for yourself ("99% of users"). Have you done a survey? Please stop this nonsense.
BTW, to me wolframalpha is just a tool. It's not the bible of mathematics. It's just a computer program. Maybe when wolframbeta goes online it does know about <>...