Question

Factor completely 3x^2 − x − 4.

(3x − 1)(x + 4)

(3x + 4)(x − 1)

(3x − 2)(x + 2)

(3x − 4)(x + 1)

Answer 1

if the 3, in ax^2, was not there...
do you know how to factor these kinds of stuff

Answer 2

\(\color{#0cbb34}{\text{Originally Posted by}}\) @snowflake0531
if the 3, in ax^2, was not there...
do you know how to factor these kinds of stuff
\(\color{#0cbb34}{\text{End of Quote}}\)
no.. 😐

Answer 3

:/, you're teacher first gave you harder thing before the fundamental stuffO-O
oof

Answer 4

\(\color{#0cbb34}{\text{Originally Posted by}}\) @snowflake0531
:/, you're teacher first gave you harder thing before the fundamental stuffO-O
oof
\(\color{#0cbb34}{\text{End of Quote}}\)
wait, actually I think ik how to do it-

Answer 5

well, would you know how to simplify each of the choices

Answer 6

\(\color{#0cbb34}{\text{Originally Posted by}}\) @snowflake0531
well, would you know how to simplify each of the choices
\(\color{#0cbb34}{\text{End of Quote}}\)
idk, im confused

Answer 7

do you know how to simplify each of these
(3x − 1)(x + 4)

(3x + 4)(x − 1)

(3x − 2)(x + 2)

(3x − 4)(x + 1)

Answer 8

yea, I think so.. correct me if im wrong, is the first one 3x^2 + 11x - 4

Answer 9

yes
and AZ will take over
he's better at explaining this kind of stuff

Answer 10

ok

Answer 11

so yeah you could do that method too but let's learn how to factor it the right way in case there isn't any answer choices

Answer 12

\(\color{#0cbb34}{\text{Originally Posted by}}\) @AZ
so yeah you could do that method too but let's learn how to factor it the right way in case there isn't any answer choices
\(\color{#0cbb34}{\text{End of Quote}}\)
ok

Answer 13

when we have
ax^2 + bx + c

where a, b, and c are just the coefficients

then when we're factoring

we have to find a number that multiplies to a*c
and adds up to b

Answer 14

so for your question 3x^2 − x − 4

3*(-4) = -12
so what two numbers multiply to give us -12

and add up to give us -1

Answer 15

I-

Answer 16

-6 x 2 = -12

Answer 17

forget about the -12

what are all the factors of 12
what two numbers can multiply to 12

Answer 18

im confused :|

Answer 19

so what are the factors of 12

like
1 * 12 = 12
2 * 6 = 12
3 * 4 = 12

Answer 20

ohhhh

Answer 21

now remember we said

\(\color{#0cbb34}{\text{Originally Posted by}}\) @AZ
so for your question 3x^2 − x − 4

3*(-4) = -12
so what two numbers multiply to give us -12

and add up to give us -1
\(\color{#0cbb34}{\text{End of Quote}}\)

Answer 22

we need to make one of the numbers negative so that way when we multiply it, we'll get negative 12

and when we add it, we'll get negative 1

Answer 23

so

do we use
-3 and 4

or -4 and 3

Answer 24

-4 and 3

Answer 25

good! so now that we have those two numbers

we can write

3x^2 - x - 4

that -x
we can re-write it as
3x - 4x
because that's equal to -x

so we have

3x^2 + 3x - 4x - 4

do you know how to factor by grouping?

Answer 26

im not sure

Answer 27

so to do it we factor it as halfs

Answer 28

so we have

3x^2 + 3x - 4x - 4


so let's factor
3x^2 + 3x

and factor -4x -4

Answer 29

3x(x + 1)

Answer 30

Good!

What about
-4x - 4

Answer 31

and -4(x+1)

Answer 32

I have to go :(

Answer 33

we're almost done!

Answer 34

ok

Answer 35

but we can finish later if you have to go go

Answer 36

\(\color{#0cbb34}{\text{Originally Posted by}}\) @AZ
but we can finish later if you have to go go
\(\color{#0cbb34}{\text{End of Quote}}\)
lets finish it bc I won't be back any time soon ;-;

Answer 37

so we went from

3x^2 + 3x - 4x - 4

to

3x(x + 1) -4(x+1)

so now we have

3x(x + 1) -4(x+1)


so now think of the (x+1) as an apple or let's use a new letter such as `c` just so that we can see everything more clearly

so we have

3x*c -4c

can you see it now?

Answer 38

can you factor out the c from

3xc - 4c

Answer 39

ah, c(3x-4)

Answer 40

exactly!! and we were just using `c` in place of (x+1) since that was so big

so essentially
c(3x-4) is (x+1)(3x-4)

Answer 41

ta-da!

Answer 42

:o tysmm

Answer 43

I get it now-

Answer 44

yay!!

Answer 45

you're most welcome :D

Answer 46

I feel so dumb 😅

Answer 47

everyone does while learning~

Answer 48

\(\color{#0cbb34}{\text{Originally Posted by}}\) @snowflake0531
everyone does while learning~
\(\color{#0cbb34}{\text{End of Quote}}\)
yeah B)

Answer 49

no no no

I was once like you too learning this and now I'm much better at it
(Like I even saw the question and was hesitant to take a stab at it because of the 3x^2 so I told snowflake to do it until I remembered and took over so don't feel bad at all!)

Answer 50

xD thx for the encouragement guys :)

Answer 51

or girls 0-0

Answer 52

you're welcome :D

Answer 53

lmao

Answer 54

We meet again o;

Answer 55

xd