Question

PLEASE HELP!!!

How do you factor 4x^2 − 6x − 4?!?!?!?!?!?!

Answer 1

use the quadratic formula
-b + or - sqrt(b^2 - 4ac) / 2a

a is the coefficient of x^2
b is the coefficient of x
c is the coefficient of x^0 (const)

Answer 2

can you show me how to do that?

Answer 3

so look it here please what terms are common

2x*2x -2x-2x-2x-2-2 ?

Answer 4

2

Answer 5

and 2x

Answer 6

yes so than factorize it out from every terms what will get ?
first just 2

Answer 7

courage this is easy

Answer 8

2(2x^2 - 3x - 2)

Answer 9

nice
so now you need working with terms inside parentheses

2x^2 -3x-2 = 2x*x -x-2x-2 =

grouping them from first 2 terms what can you factoriz out and from 3rd and 4th ?

Answer 10

2

Answer 11

so 2 just from 3rd and 4th but from first and second ?

Answer 12

so for 2x^2 -3x -2 make it equal zero and using discriminant method can you get the roots of this quadratic ?

Answer 13

what?

Answer 14

what is formula for discriminant ?

Answer 15

the quadratic formula

Answer 16

D=b^2-4ac

can you calculi it ?

Answer 17

-28

Answer 18

how you have got it ?

Answer 19

b^2 = ?

Answer 20

-6

Answer 21

oh sorry 36

Answer 22

no
you work now just with quadratic inside paretheses

Answer 23

parentheses - sorry

Answer 24

2x^2 -3x -2 =0
D=?

Answer 25

I'm sorry, I don't understand

Answer 26

so first in case of initial quadratic you have factorized out 2 - yes ?

Answer 27

right

Answer 28

oh, I get it

Answer 29

than calculi it please

Answer 30

okay hold on

Answer 31

can you solve it sure till end ?

Answer 32

is it 25

Answer 33

?

Answer 34

yes and x_1,2 = ?

Answer 35

what does x_1,2 mean?

Answer 36

the roots of this quadratic inside parentheses

Answer 37

oh

Answer 38

they're -1/2 and 2

Answer 39

right?

Answer 40

how you have got these roots ?

Answer 41

-b +/- sqrt(D)
x_1,2 = --------------
2a

do you know this formula ?

Answer 42

no

Answer 43

wait, is that the quadratic formula?

Answer 44

yes

Answer 45

so using this formula what roots will get ?

Answer 46

um, hold on

Answer 47

2x^2 -3x -2 =0
D=25
3 +/- 5
x_1,2 = --------- = 2 and -1/2
4

right ?

Answer 48

so this mean that your results was right but how you have got them ?

Answer 49

yes I got -1/2 and 2

Answer 50

so now using these roots you can rewriting the quadratic factorized -

Answer 51

how will be ?

Answer 52

um, I'm not sure

Answer 53

why ? try it please

Answer 54

us formula

Answer 55

what do you mean by rewriting the quadratic formula?

Answer 56

rewriting the quadratic using formula (x-x_1)(x-x_2)

do you know this ?

Answer 57

oh, so (x - 2)(x + 1/2) ?

Answer 58

so for you can being sure that is right you can check it - yes ?

Answer 59

how do you check it?

Answer 60

multiplie term by term and look than you will get the necessary quadratic

Answer 61

okay I got x^2 - (3x/2) - 1, but that's not the original

Answer 62

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

yes for you can eliminate the denominator what you need to do ?

Answer 63

2x^2 +x -4x -2
-------- + -------- = ?
2 2

Answer 64

(2x + 1)(x - 2)/2

Answer 65

in numerator you get

2x^2 -3x -2 the quadratic from what you have started your calculi

than this mean that this quadratic is factorized completly will be (x-2)(x + 1/2)

but dont forget that in the first step you have factorized the 2

so than what will be your exercise solved right ?

Answer 66

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

Answer 67

yes but than you dont believe it make the prove of making the calculi multiplid term by term and you need getting the original quadratic

ok ?

Answer 68

ok.

Answer 69

thank you :)

Answer 70

was my pleasure - hope so much that now you understand it sure right how you need solving same exercises - yes ?

Answer 71

yes I understand it now

Answer 72

ok. good luck

bye