Question

can someone help me with the factor of 6m^2+4m-16 i don't want the answer I want someone to help me threw the steps and help me if I mess up please

Answer 1

Use quadratic formula x = -b + or - the square toot of b^2 - 4ac all over 2a werer a=6 b=4 and c=16

Answer 2

There is a little known method called the slide and divide method that you might find interesting. See here: http://algebrafunsheets.com/blog/2008/11/22/slide-and-divide-method-of-factoring-trinomials/

Let me know if you need any help in understanding that method.

Answer 3

or you can factor find your factors of 6 and your factors of 16 the sum or difference of your factors should equal 4

Answer 4

ok im stuck on this

Answer 5

have you looked at the link I gave above?

Answer 6

yes ok so ac is 6*1 and b is 4

Answer 7

where did you get that from?

Answer 8

the equation you are trying to factor is:\[6m^2+4m-16\]correct?

Answer 9

yes

Answer 10

so, if you read that link, the first thing it asks you to do is:
"(Always ensure to pull out any common factors before continuing with this method)"

Can you see a common factor across all terms in your equation?

Answer 11

the m and maybe 4 and 16

Answer 12

"m" does not divide into ALL the terms - so it cannot be a common factor
same goes for 4 and 16

find a factor that divides into ALL the terms

Answer 13

what divides into all these terms: \(6m^2, 4m\) and \(16\)

Answer 14

hint: 6, 4 and 16 are all EVEN numbers so they they can ALL be divided by ?

Answer 15

2

Answer 16

great!

Answer 17

so now we can first rewrite your equation as:\[6m^2+4m−16=2(3m^2+2m-8)\]agreed?

Answer 18

yes i see how you did that

Answer 19

ok good, so now we can just concentrate of factoring this:\[3m^2+2m−8\]

Answer 20

now the slide and divide method says that we first take the coefficient of \(m^2\) and "slide" it over to the "constant" term using multiplication

Answer 21

so here we need to remove the 3 from \(3m^2\) and "slide" it over to the "-8" replacing "-8" with "-8"*3 = "-24"

Answer 22

that will leave us with:\[m^2+2m-24\]agreed?

Answer 23

yes

Answer 24

ok, the next step is to then try to factor this expression - which should be a lot simpler.
we need to find the ?'s in this expression:
\(m^2+2m-24=\)(m ?)(m ?)

Answer 25

so, can you think of two number that when multiplied together give you 24?

Answer 26

i.e. find all the factors of 24

Answer 27

you would then pick out those two factors that can also be combined (i.e. added or subtracted) to give you 2 (for the \(2m\) term)

Answer 28

e.g.
a) 24 = 1 x 24 but 24 and 1 cannot be combined to give you 2 - so we reject these two
b) 24 = 2 x 12 but " ... "
etc

Answer 29

24= 3 x 8
24=4 x 6

Answer 30

good - so which of those give you factors that can be combined to give you 2?

Answer 31

combined as in added or subtracted

Answer 32

4 and 6

Answer 33

perfect - and how can we get 2 by combining 4 and 6?

Answer 34

-4 + 6

Answer 35

great! so now we can write:\[m^2+2m-24=(m-4)(m+6)\]agreed?

Answer 36

yes thats what i got :)

Answer 37

perfect! :)

now the next step is to divide the constants in this expression by the number we "slid" over at the beginning - in this case we slid over 3, so we need to divide the constants by 3 and then simplify to get:\[(m-\frac{4}{3})(m+\frac{6}{3})=(m-\frac{4}{3})(m+2)\]do you follow?

Answer 38

not really

Answer 39

do you remember we "slid" over the 3 at the beginning?
recall we started with:\[3m^2+4m-16\]

Answer 40

yes o ok so now we use the 3

Answer 41

sorry I mean\[3m^2+2m-8\]

Answer 42

let me list the steps from the start just to clarify for you...

Answer 43

ok

Answer 44

\[\begin{align}
6m^2+4m-16&=2(3m^2+2m-8)\\
\text{next we slide over the 3 to get:}\\
m^2+2m-24\\
\text{we then factorised this to get:}\\
(m-4)(m+6)\\
\text{we now divide by 3 - the number we slid over:}\\
(m-\frac{4}{3})(m-2)
\end{align}\]

Answer 45

the lines shown above from line 2 onwards are intermediate steps we need to do in order to factorise \(3m^2+2m-8\)

Answer 46

ok

Answer 47

the final step says that if you get left with any fractions (as we have), then you take the denominator of the fraction and move it over to the "m" term, so the term:\[m-\frac{4}{3}\]becomes:\[(3m-4)\]we can then conclude that:\[3m^2+2m-8=(3m-4)(m+2)\]NOTE: I made a mistake on my last line above - (m-2) term should have been (m+2)

Answer 48

putting it all together we get:\[6m^2+4m-16=2(3m^2+2m-8)=2(3m-4)(m+2)\]hope that makes sense.

Answer 49

I would advise you to re-read that link I gave above and try some more examples of your own to become familiar with this method.

Answer 50

the best way to generate examples is to start from what you want the answer to be and expand it - then see if your factorisation process leads to the same answer.

e.g. \[(2x+3)(x-5)=2x^2-7x-15\]so see if you can use this method to factorise \(2x^2-7x-15\)

Answer 51

ping me if you need more help in understanding this - and good luck! :)

Answer 52

thanks so much and i will

Answer 53

ok - and keep at it my friend - practice makes perfect! :)

Answer 54

ok im stuck on the one that you wanted me to try i think i am doing it right but im not shore

Answer 55

please list your steps so I can then try to spot where you may have made a mistake

Answer 56

ok

Answer 57

2x^2-7x+30
2x^2-7x+30 = (x+10) X-3)
10m-2 = 5

Answer 58

it should be "2x^2 - 7x - 15" at the start

Answer 59

o yea i did have that down i typed it wrong sorry

Answer 60

ok let me re type it

Answer 61

you also had a plus sign instead of a minus sign

Answer 62

2x^2 - 7x - 15
x^2-7x+30 (x+10) (x-3)
10x-2= 5

Answer 63

you've made the same mistake here -> the second line should have a "- 30" not a "+ 30"

Answer 64

let me do this one for you and I'll give you another one to try...