Question

Factor completely: 3x2 - x - 4

Answer 1

(x+1)(3x−4)

Answer 2

How did you get that?

Answer 3

I just used this: https://www.mathway.com/
Much easier and faster than solving it on paper.

Answer 4

(3x - 1)(x + 4)

(3x + 4)(x - 1)

(3x - 2)(x + 2)

(3x - 4)(x + 1)

These are the answers I can choose from though

Answer 5

So it's just the other way around?

Answer 6

The answer's D :)

Answer 7

Yeah the other way around. C:

Answer 8

thx @maria195 wow such a cheater

Answer 9

@amistre64 can you explain it to me

Answer 10

@camerondoherty

Answer 11

@yamyam70

Answer 12

@iGreen

Answer 13

could you guys explain why is this the answer

Answer 14

i dont understand how can this be the answer

Answer 15

what does it mean to be a factor?

Answer 16

@Law&Order try using the FOIL method, to check

Answer 17

i dont know how

Answer 18

resolve or be resolvable into factors

Answer 19

if i ask you what are the factors of 25, what am i asking for?

Answer 20

the factors are 5*5

Answer 21

so, what you have done is to split it up into multiplication, right?

Answer 22

yes, ok im getting it

Answer 23

Step 1 :
Simplify 3x2-x - 4


Trying to factor by splitting the middle term

1.1 Factoring 3x2-x-4

The first term is, 3x2 its coefficient is 3 .
The middle term is, -x its coefficient is -1 .
The last term, "the constant", is -4

Step-1 : Multiply the coefficient of the first term by the constant 3 • -4 = -12

Step-2 : Find two factors of -12 whose sum equals the coefficient of the middle term, which is -1 .


-12 + 1 = -11
-6 + 2 = -4
-4 + 3 = -1 That's it


Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -4 and 3
3x2 - 4x + 3x - 4

Step-4 : Add up the first 2 terms, pulling out like factors :
x • (3x-4)
Add up the last 2 terms, pulling out common factors :
1 • (3x-4)
Now add up the four terms of step 3 :
(x+1) • (3x-4)
Which is the desired factorization

Final result :
(3x - 4) • (x + 1)

Answer 24

\(\huge\ddot\smile\)

Answer 25

is that tiger algebra

Answer 26

when we factor something like:

3x2 - x - 4

we want to turn it into a multiplication setup

(this) (that)

Answer 27

yup :)

Answer 28

im sorry but i dont understand

Answer 29

lol

Answer 30

oh @amistre64

Answer 31

so we split it up

Answer 32

but how @amistre64

Answer 33

there are a few methods to approach it, but all of them are a bit involved and assume you have a basic knowledge of algebra to play with

Answer 34

yes i think i know

Answer 35

but there is a way that i did it but it gave me the wrong answer
3x^2-x-4
then i split it to
x(3x+3)-2(2x+2)

Answer 36

lets assume it factors into something like:

(ax+b) (cx+d); we can then expand this out to compare parts with

ax+b
cx+d
-------
acx^2 + bcx
+adx +bd
--------------------
acx^2 +(ad+bc)x + bd

which may or maynot be practical, but it helps see the mechanics going on

Answer 37

\(\color{green}{\huge\cal 3x^2-x-4}\)
\(\color{green}{\huge\cal x(3x+3)-2(2x+2)}\)

but you cant make it simplifyed because the two parenthesis isnt the same

Answer 38

mm hm

Answer 39

*nods head*

Answer 40

by comparison of like terms we have:

3 x^2 -1 x - 4
ac x^2 +(ad+bc)x + bd

ac = 3; let c = 3/a
bd = -4; let d=-4/b

ad + bc = -1

-4a/b + 3b/a = -1

-4a + 3b^2/a = -b

-4a^2 + 3b^2 = -ab

so yeah, this approach doesnt seem practical to me.

Answer 41

my own prefered method, assuming at factors into rationals is:

multiply first and last

3 x^2 - x - 4 ; 3(-4) = -12

since its negative we have opposite signs

(x+ p/3) (x- q/3) will be the setup, p and q are factors of 12

since the middle term is a negative value, the bigger term is the negative

4,3 are factors of 12, and -4+3 = -1 sooo

(x+ 3/3) (x- 4/3) , simplify

(x+1) (x- 4/3) , if theres still a fraction, put the bottom back in front

(x+1) (3x- 4)

Answer 42

thats my take on it, since i am no good at factor by grouping :)