Question

http://prntscr.com/atkxbl

Answer 1

im confused

Answer 2

you see any common factors in \(6x+8\)?
hint, both coefficients are even

Answer 3

2?

Answer 4

yes
"factor it out" as the math teachers say

Answer 5

i don't have a teacher that i communicate with .-. online school

Answer 6

how do i factor it out tho @Kainui

Answer 7

lucky you

Answer 8

just change \(6x+8\) in to \(2(3x+4)\)

Answer 9

oh yeah

Answer 10

wait where did u even get 6x+8 tho

Answer 11

dividing the things by 6?

Answer 12

i didn't get it
it was written in your question

Answer 13

the only part where i see that is in line 4

Answer 14

we are trying to see if she factored http://prntscr.com/atkzis correctly right

Answer 15

All of the steps are written out in the picture, so here's a strategy to help you figure it out:

Look at step 1 and step 2. What stayed the same? What changed? The steps are reversible, can you go from step 2 to step 1? Can you go from step 1 to step 2? If you can do one of these directions you will be able to figure out how to do the reverse.

Answer 16

ok hold on lemme look at that

Answer 17

wait why did 76 split into 36 and 40 tho

Answer 18

i was never taught this

Answer 19

Replace "x" with "apples" just for your own mental satisfaction, it really doesn't change anything. Then you have 76x turning into 36x + 40x. So are 76 apples the same as 36 apples + 40 apples??

Answer 20

well yes

Answer 21

depends on what kind of apples tho

Answer 22

There are no apples, so it doesn't matter. You're counting number of x's not number of apples.

Answer 23

ok so no apples, I can see which steps are being taken to factor it

Answer 24

but idk if its correct or not

Answer 25

i know the second half is right

Answer 26

6x(5x + 6) directly contradicts 8(5x +6) because it is 30x^2 and the second part is just 40x

Answer 27

right? @Kainui

Answer 28

sorry if i don't know simple stuff I'm only in 9th xD

Answer 29

My computer died I forgot to plug it in haha.

So I was just gonna say don't get confused about the notation, \(5x\) means you have literally added 5 of the xs together, that's why this is equal:

\[5x=x+x+x+x+x\]

Same exact thing, so I just want to make that clear, the 5x is like shorthand for writing out all 5 xs at once haha. I sure wouldn't want to write out 30x.

Ok moving on, I'm not sure what you are saying about contradicts, so tell me what steps you're looking at specifically, are you looking at the step from Line 2 to Line 3 or from Line 3 to Line 4?

Answer 30

well we could copy n paste x + ok getting off topic, but I'm saying from line 2 to 3

Answer 31

since if 30x^2 + 36x would factor into 6x(5x + 6)

Answer 32

then it can't possibly be 40x + 48 factoring into 8(5x +6)

Answer 33

because the first one is squared

Answer 34

@Kainui

Answer 35

Looks you trying to match first half and second half. Why do you think they must be equal ? Only things that stand on either side of equality need to be equal. First half and second half in any expression need not be equal...

Answer 36

well i was just saying that the method of factoring should probably be different if its a different kind of number

Answer 37

but I'm no expert in math so can u teach me xD

Answer 38

Btw, there is a step missing between the lines 2 and 3. They skipped the grouping step and I think this is the reason his solution is confusing...

Answer 39

Did you get how line2 follows from the line1 ?

Answer 40

yes, the 76x got cut into 2 unequal pieces

Answer 41

Nice. He took line2 and grouped first two terms and last two terms before factoring out the GCF in each group :

line2 :
30x^2 + 36x + 40x + 48

line2a :
(30x^2 + 36x) + (40x + 48)

Answer 42

whats the GCF of the terms in first group ?

Answer 43

yeah the GFC

Answer 44

GCF*

Answer 45

its 6 right

Answer 46

6 is common from numbers
what about x's ? looks you can pull out an x too

Answer 47

2x?

Answer 48

Not quite. look at the expression 30x^2 + 36x

```
30 and 36 have 6 in common
x^2 and x have x in common
```

so we can rewrite it as 6x*5x + 6x*6
pull out the common 6x and get 6x(5x + 6)

Answer 49

yes yes

Answer 50

i still don't know if she did it correctly or not xD

Answer 51

just to double check, multiply it and see if you get back the stuff you have started with

Answer 52

6x(5x + 6) = ?

Answer 53

30x^2+36 right @ganeshie8

Answer 54

that is same as the first group, so we're good.
Look at second group next

Answer 55

OHHHH I SEE IT NOW DUDE

Answer 56

(30x^2 + 36x) + `(40x + 48)`

Answer 57

40x + 48

whats the GCF of these two terms ?

Answer 58

the first part had 2 x's and the second part only has 5x, UR A GENIUS

Answer 59

its 8

Answer 60

its factored correctly right

Answer 61

that part

Answer 62

yea so the second group factors as 8(5x+6)

Answer 63

yes it does

Answer 64

line2 :
30x^2 + 36x + 40x + 48

line2a :
(30x^2 + 36x) + (40x + 48)

line3 :
6x(5x + 6) + 8(5x + 6)

Answer 65

im not sure about line 4

Answer 66

Look at line3 now
see anything common between the two groups ?

Answer 67

6x(5x + 6) and 8(5x + 6)

take a good look, see anything common ?

Answer 68

5x+6

Answer 69

Yes pull that out, what do you get ?

Answer 70

6x +8?

Answer 71

pulling that out doesn't mean you throw that in garbage

Answer 72

6x(5x + 6) + 8(5x + 6)

pulling the common 5x+6 out gives
(5x + 6)(6x + 8)

5x+6 sticks with the expression ok

Answer 73

yes, it sticks

Answer 74

OH I SEE IT NOW

Answer 75

just know that math has few rules, play by those and you will be fine :)

Answer 76

"few"

Answer 77

so we see that there is nothing wrong in his work, now lets try and answer A

Answer 78

Vicky is a guy??? :P

Answer 79

ikr thats what i was thinking .-. @Kainui

Answer 80

vicky is a guy name in india...

Answer 81

WOAH

Answer 82

ok Vicky correctly factored

Answer 83

but did she do it completely

Answer 84

hold on lemme see

Answer 85

im not sure

Answer 86

yeah look at satellite's first reply

Answer 87

oh so its no

Answer 88

that is the only thing you need to answer part A

Answer 89

because there are still common factors

Answer 90

Yea he/she followed all the rules correctly and factored almost completely. But he/she forgot to factor the GCF for the terms in line1

Answer 91

yes so i put Vicky factored correctly, but not completely, there are still common factors for (6x + 8)

Answer 92

look at the starting line1

is there anything common in all the terms ?

Answer 93

well theres 2

Answer 94

Yes, that should be his/her first step. Instead of rushing to split that middle 76x, he should have checked for any common terms in the given expression. This should always be your first step while factoring polynomials or similar things..

Answer 95

yes correct

Answer 96

factor it completely and see what you get

Answer 97

what do u mean, the last line? or starting from first