Question

Select one of the factors of 3x2 + 4x - 4.
(x + 4)
(3x + 2)
(3x - 2)
(x - 2)

Answer 1

can you find 2 numbers whose sum is +4
and product is 3(-4) = -12 ?

Answer 2

wait what? lol i remember something about that but can you explain as to what exactly i have to do?

Answer 3

sure :)

to factor \(ax^2+bx+c\)

we split the middle term : bx

by finding 2 numbers with sum as +b
and product as ac

Answer 4

so for
\(3x^2 +4x-4\)
we need to split 4x

find 2 numbers with sum as +4
and peoduct as -12

Answer 5

*product

Answer 6

I see why you would try to find 4 but why -12?

Answer 7

oh wait is it becuase you have to multiply 3 & 4

Answer 8

yes
ac = 3(-4) =-12

so that we would be able to factor out the quadratic into 2 factors properly

Answer 9

oh okay that makes sense.

Answer 10

so...

can you find 2 numbers whose sum is +4
and product is 3(-4) = -12 ?

Answer 11

hint : one number is negative, other is positive

Answer 12

6\[6-2=4 and 6\times-2\]

Answer 13

good!

so we split 4x as
\(\large 4x =6x -2x\)

Answer 14

\(\Large 3x^2 +6x-2x-4\)

what can you factor out from 1st 2 terms
\(3x^2 +6x\)
??

Answer 15

sorry i had to answer the phone

Answer 16

\(\Large 3x^2 = 3x (x) \\ \Large 6x = 3x(2)\)
no problem!

Answer 17

this is where i get stuck. so would you do this?

Answer 18

\[3x(x+2)?\]

Answer 19

yes!

Answer 20

so,

now take last 2 terms
-2x-4

what can you factor out ?

Answer 21

-2(x-2)?

Answer 22

-4 is actually -2(+2)
not
-2(-2)

Answer 23

oops sorry

Answer 24

so
\(\Large -2x-4 = -2 (x+2)\)
makes sense ?

Answer 25

yes

Answer 26

we have now
\(\large 3x\color{blue}{(x+2)} -2 \color {blue}{(x+2)}\)
what can be factored out ??

Answer 27

(x+2)(3x-2)?

Answer 28

\(\Huge \checkmark \)

Answer 29

awesome thank you!!!

Answer 30

welcome ^_^