Question

I need help with reversing the FOIL method.
equation: 4x^3+3x^2+20x+15

Answer 1

grouping ....

Answer 2

4x^3+3x^2+20x+15

group it with ( )s

(4x^3+3x^2) + (20x+15)

now take out the commons for each set of ()

Answer 3

dumb it down a little bit what do you mean by take out the commons ?

Answer 4

what is the common factor of 4x^3 and 3x^2?

what is the common factor of 20x and 15?

Answer 5

greatest common factor lowest common factor what kind?

Answer 6

thats a fair question ... we would want to take the greatest common factor in or to be able to reduce them to a simplest form

Answer 7

*in order to ...

Answer 8

I don't know how to do this im so lost.

Answer 9

this would have been practiced a ton before ever getting to this type of question. I am assuming that you have been exposed to the simpler processes and I am simply trying to get you to apply what you would have already known.

Answer 10

im just new to this Reverse FOIL thing

Answer 11

what is the common factor of 4x^3 and 3x^2?

4xxx and 3xx have xx in common; so x^2 can be factored out

(4x^3 + 3x^2) = x^2(4x+3)



what is the common factor of 20x and 15?

4*5x and 3*5 have 5 in common, so we can factor that out

(20x + 15) = 5(4x+3)

Answer 12

FOIL is a memory device, and should never be taught in my opinion. If you know the distributive property, then you can work this all out

Answer 13

the distributive property:

a(x+y) = ax+ay

if we have ax+ay, we can undistribute it by factoring out its common factor:

ax+ay = a(x+y)

Answer 14

so far we have worked it up as:

\[4x^3+3x^2+20x+15\]
\[(4x^3+3x^2)+(20x+15)\]
\[x^2(4x+3)+5(4x+3)\]
from here we should be able to see that both terms have (4x+3) in common; but if you want to see it better, let a = (4x+3)
\[x^2a+5a\]
in other words, lets "undistrbute" that a
\[a(x^2+5)\]
and since we defined a to be (4x+3)
\[(4x+3)(x^2+5)\]

Answer 15

I see how you got it. but lets practice another?

Answer 16

one more then :)

Answer 17

40n^3-20n^2+32n-16 lets take it slow step by step

Answer 18

(40n^3-20n^2) (32n-16) ?

Answer 19

dont run over that + sign
v
(40n^3-20n^2) + (32n-16)

but yes, so far so good

Answer 20

40nnn and 20nn simplifies to (40n+20)?

Answer 21

go ahead and undistribute the nn, but there is still more they have in common; 40 = 20*2

40nnn and 20nn; 20nn in common 20n^2(2n-1) is better

Answer 22

so now we gotta see what 32n and 16 have in common? which would be 8? which would give you 4n-2?

Answer 23

no
2n-1

Answer 24

2 and 4 still have a common factor so its not in simplest form yet

32n and 16

16*2n and 16n have 16n in common reducing to (2n-1) which is what we would expect to happen

Answer 25

ugh, typed in that n by mistake

Answer 26

edit****

16*2n and 16n have 16 in common reducing to (2n-1) which is what we would expect to happen

Answer 27

so now we have 20n^2(2n-1)(2n-1)?

Answer 28

now lets see it in a big picture:

\[40n^3-20n^2+32n-16\]
\[(40n^3-20n^2)+(32n-16)\]
\[20n^2(2n-1)+16(2n-1)\\~~~~~~~---~~~~~~~~~~---\\~~~~~~~~~~~~a~~~~~~~~~~~~~~~~~~~~a\]

Answer 29

UGH I I don't know what to do on tis last step.

Answer 30

since they have a common factor "a", undsitribute it

Answer 31

\[20n^2(2n-1)+16(2n-1)\\~~~~~~~---~~~~~~~~~~---\\~~~~~~~~~~~~a~~~~~~~~~~~~~~~~~~~~a\]

\[20n^2a+16a=a(20n^2+16)\]

Answer 32

im lost on this last part with the "a"

Answer 33

i actually have to go to lunch then switch classes ill be back at 12:15 eastern time ill come back. talk to you then. :(

Answer 34

with a lot of practice on these, you can learn to see the common factor; im just trying to clean it up visually so that it is simpler to assess.

the distributive property is defined as:

a(x+y) = ax+ay, this is a fundamental property of algebra.

we can "undistribute" ax+ay back into the form a(x+y) by factoring out the common "a"

Answer 35

FOIL is a memory device that uses the distributive property:

for example:

(x+2) (5x-3) ; let a = (x+2)

a(5x-3) = 5xa -3a

we now have 2 more distributions to accomplish since a = (x+2)

5x(x+2) -3(x+2)

5x(x) + 5x(2) -3(x) -3(2)

5x^2 + 10x -3x - 6

5x^2 + (10-3)x - 6

5x^2 + 7x - 6

Answer 36

Here is a link: http://www.youtube.com/watch?v=162ub1GIuqA.
It's the same explanation as amistre64 but it might help you to see someone explaining it as a video.
Also you might want to look up factoring using polynomial long division. Sometimes it's easier to factor a third degree polynomial that way.