Question

6 + 10 x + 14 x^2

what's the GCF here and is it smaller than the smallest coefficient?

Answer 1

2 see it as GCF = 2

Answer 2

1,2,3,6 is the best you can get, what number do the rest have in common with this?

Answer 3

I'm thinking

Answer 4

....think....quieter.....

Answer 5

It hurts....

Answer 6

I am not sure...why do I not get this stuff?

Answer 7

tell me, what are the coeeficients?

Answer 8

2

Answer 9

2 is a coefficient?

Answer 10

I know whatever it is is not smaller then it is, because they are equal to each other...just not sure what number

Answer 11

it is 6?

Answer 12

6 is the smallest coefficient..yes; so any factors cannot possibly be larger than 6.

Answer 13

Thank you so much..sorry about any trouble I caused

Answer 14

think of it this way:

if someone wants you to give them $10 and all you have is $3; what is the most you can give them?

Answer 15

3

Answer 16

exactly; so, in this problem of yours we have some numbers that are carrying cash...

the largest amount of cash that they have in common cant be greater than the "$6" number right?

Answer 17

right

Answer 18

so lets open up that "$6" dollars wallet and see what hes got in there...

hes got the following bills:

$1, $2, $3 , $6. the rest of the numbers have similar types of cash. but the biggest numbered bill they have in common is a $2.

Answer 19

I get it....that sounds simple...till you get to the way it looks in front, if they would word the things like you just did, I would be fine...

Answer 20

the "10" is carrying:

$1, $2, $5, $10

the "14" is carrying:

$1, $2, $7, $14

the only "bills" they have in common are $2 bills

Answer 21

Maybe you can help me with the next 2 things, do you have time?

Answer 22

I wish you were my teacher.....

Answer 23

i got at most an hour and a half :)

Answer 24

only 2 small questions left....

Answer 25

what are the different ways a quadratic polynomial can be factored out. What applies when?

Answer 26

and..........

x ^ 3 + 2x^2 + x = 0

Can factorization still help solve this equation ? If yes, how ?

Answer 27

Those are it...If you have time.

Answer 28

lets dooooo this!!! ... :)

Answer 29

thats my machoman randy savage impersonation :)

Answer 30

what are the different ways a quadratic polynomial can be factored out. What applies when?

the different ways to factor a quad equation..... well, there is the trial and error method

Answer 31

I love your enthusiasm:)

Answer 32

lol

Answer 33

I think they should put a like button on here!lol

Answer 34

there is the "completeing the square" method

Answer 35

hah...i think thats the fan button. they give you cool titles like lifesaver, champion, star...but when you get to 100 and above, they turn you into a sandwich :/

Answer 36

:( (to the sandwich part) I'm a fan of you:)

Answer 37

I suck i have no fans

Answer 38

awww.... thanx :) I hit 200 a few days ago and was hoping for something cool like "turkey club on rye"..but noooooo.....they stuck me with "superhero" lol

Answer 39

be right back...I need to check on my daughters...

Answer 40

lol...

Answer 41

ok..they are fine

Answer 42

the four most used methods to factor quadratics are:

Factoring
Factor by Grouping
Quadratic Formula
Completing the Square

Answer 43

Does that have to do with the 1st question

Answer 44

When do we use them? dunno really.

Factoring is just splitting it up into its basic components... that can be done if its easy to recognize

Answer 45

yeah sure...maybe :)

Answer 46

by grouping generally ocuurs when there are more than 3 terms. we group them into pairs and factor them seperatley

Answer 47

the quad formula is used when we just dont have time or patience to do the other ways :)

Answer 48

and completing the square is just the long hand version of the quad formula, I guess you use it when you cant recall the quadratic formula :)

Answer 49

Now to the 2nd question

Answer 50

x ^ 3 + 2x^2 + x = 0

Can factorization still help solve this equation ? If yes, how ?

Yes, if we can notice that all the terms include an "x" factor then we can remove it and do our quadratic techniques on the remaining terms like this:

x ^ 3 + 2x^2 + x = 0

x(x^2 +2x +x) = 0
x (x+1)(x+1) = 0

x = 0 or x = -1

Answer 51

that little straggling +x should be a +1....

Answer 52

x(x^2 +2x +x) = 0 <- right in there

x(x^2 +2x +1) = 0
x (x+1)(x+1) = 0

Answer 53

ok, Now I am confused...

Answer 54

lol...story of my life

Answer 55

tell me whats got you confused :)

Answer 56

about the straggling....

Answer 57

I had a typo in there; that x^2 +2x +[x] <- right there.

it should have been: x^2 +2x +1

Answer 58

Thank you got it! I will probably be on again tomorrow.....I have this stuff all week and get really frustrated! Thanks for all your help! You are great! I am sure you are better then a sandwich:)

Answer 59

thanx :) take care ;)

Answer 60

You too