Question

What is the factorization of 4x^2-31x+21?

Answer 1

please don't leave, we want to help you. Many people like

(4x-3)(x-7)

Answer 2

people like you left OS, because of small (as they though) inconveniences.

Answer 3

@MaxRide

Answer 4

I'm not planning on leaving if this helps me.

Answer 5

Good, b/c it does help you :) See, how I am tagging you ? You welcome!

Answer 6

Um, aren't the -3 and -7 supposed to add up to -31?

Answer 7

( 4 x - 3 ) (x - 7 ) = 4 x ( x - 7 ) - 3 ( x - 7 ) =
4x^2-28x - 3x + 21 =

4x^2-31x + 21 .

Answer 8

-3 and -7 when you multiply , the middle terms are supposed to add up to 31.
also,
-3 and -7 are suppose to be factors of 21, and yes, (-3) * (-7)= 21

Answer 9

Hang on one second.

Answer 10

Sure....................

Answer 11

Ok, now I feel completely dumb. I forgot about the 4.

Answer 12

it's okay... so do you get it, or need a little more help ?

Answer 13

I think I get it, I'll try a few more problems and be back if I need more help.

Answer 14

Thank you so much!

Answer 15

You welcome, it is totally my pleasure, and my practice :)

Answer 16

Haha.

Answer 17

☻

Answer 18

I'm doing problems 34 to 51, so instead of typing a problem out, I'll say the number, it you don't mind.

Answer 19

If I'm wrong, I'll sound stupid, but is 34 prime?

Answer 20

Never mind.

Answer 21

34 is not prime,
(3x+1)(2x+7) is the factorization... also, if the discriminant is a perfect square than it is factor-able and if the discriminant is not a perfect square then it is not factor-able.

Answer 22

Which number is the discriminant?

Answer 23

have you ever worked with a quadratic formula ?

Answer 24

I don't believe so.

Answer 25

I will show you it fast...

\(\Large\color{blue}{ \bf -3x-x+2=0 }\) is the quadratic equation.

One of the approaches to solve is it, is the quadratic formula, below in red

\(\Large\color{red}{ \bf x= \frac{ \sqrt{b^2-4ac} }{2a} }\)

Answer 26

the discriminant is the number inside the square root

Answer 27

what are the abc ?

ax^2 +bx+c=0 is the standard form, COMPARE...
-3x -x +2=0

so
a=-3
b=-1
c=2

Answer 28

So your problem.. in order to say that it is unfactorable, you must show that

b^2-4ac (in your case, (-1)^2 - 4(-3)(2) ) is not a perfect square, in other words, that it won't equal an integer after the root is taken.

Answer 29

(-1)^2 - 4(-3)(2) = 1 + 24 = 25.

we know that √25= ±5, so it's therefore a perfect square and therefore

-3x^2-x+2 is NOT PRIME.

Answer 30

Where did you get the (-1)^2 - 4(-3)(2) from?

Answer 31

Was that from my problem?

Answer 32

-1 is "b"
(-3) is "a"
2 is "c"

yes, we are doing 51, aren't we ?

Answer 33

Sorry, I was working on some problem with my dad while you were explaining that and lost track of which problem we were on. My bad. Oops!

Answer 34

a, b, and c, is referring to the red formula I posted before... the part inside the square root. Which is,
b²-4ac

Answer 35

Ok, I see it now.

Answer 36

So, your polynomial is factorable, in 51, right ?

Answer 37

trinomial

Answer 38

Yes.

Answer 39

Kay, I'm guessing I'm wrong.

Answer 40

OK, so lets think how to factor it....
- 3x² - x + 2 = 0

the approach I am going to take is to factor it out of -1 first to make it look better ;)

3x² + x - 2 = 0
(-1)(3x - 2 ) (x +1 )=0

so knowing that, we can multiply either of the factors ( "(3x - 2 )" or "(x +1 )" times -1 )

so the answer can be
(- 3x + 2 ) (x +1 ) or
( 3x - 2 ) ( -x - 1 )

Answer 41

Are you just adding the =0 to the end for my/your sake, or is that supposed to go on the end?

Answer 42

for our sake :) to have a better conceptual understanding of how I can factor out of -1.

Answer 43

The answers I already said, and there don't involve any zeros what so ever.

Answer 44

I'm gunna type it out, tell me if I'm wrong, please.

Answer 45

What are you going to type out ?

Answer 46

-3x^2-x+1
-1(3x^2+x-2)
Ignore the -1 for now.


Ok, I'm officially lost, where do I go from here?

Answer 47

then I am just factoring it....

Answer 48

I am factoring "(3x^2+x-2)" = (3x - 2 ) (x +1 ).

Now, I am saying that you can multiply either one of the factors ( "(3x - 2 )" or "(x +1)" ) by -1, (to get the -1 back) and get the final answer.
(the rule to understand this would be that -1(a)(b)=(-a)(b) or (a)(-b) )

so, it would therefore be (-a)(b) or (a)(-b) in your case,

(- 3x + 2 ) (x +1 ) or
( 3x - 2 ) ( -x - 1 )

Answer 49

I think I've got it. If I'm wrong your going to think I'm the most stupid person on the planet.

My final answer would be -1(3x-2)(x+1), right?

Answer 50

well, it is not wrong, it is just that it is technically never written like this.

Answer 51

Ok. As long as it's not wrong, I'm good for now.

Answer 52

If I'm annoying you with my questions, let me know. It's just sometimes hard for my parents to understand what is frustrating me. Thanks for sticking around for so long.

Answer 53

Um, if I finish before you leave, would you be willing to check the even numbers for me? The odds are in the book. If not, that's ok, I'll check them on Monday with my teacher.

Answer 54

@student_basil

Answer 55

you aren't annoying me, I am just making a small tutorial at the moment:)

Answer 56

Ok.

Answer 57

I am done.

Answer 58

Cool beans.

Answer 59

Could you take a peek at #40? Thnx.

Answer 60

Ok...

tell me if the discriminant of this is a perfect square or not. In other words can the trinomial in num 40 be factored or not.

Answer 61

No?

Answer 62

11²-(4)(6)(4)
121-96
25

is 25 a perfect square ?

Answer 63

Yes.

Answer 64

Where did the 11^2 come from?

Answer 65

remember the "discriminant in the quadratic formula, b²-4ac ?

Answer 66

Right, got it.

Answer 67

yes, so you have a couple ways to factor it.

way 1: (if you really not in the mood to think) set the trinomial equal to zero and solve for x, lets call the number you get for x, "h" and "k" so the factored trinomial can be written as (x-h)(x-k)

Answer 68

you can solve for x (in way 1, ) using a quadratic formula,

\(\Huge\color{blue}{ \bf x=~\frac{-b±\sqrt{b^{2}-4ac} }{2a} }\)

Answer 69

tell me if you can do way 1 or not...

Answer 70

Give me a minute to attempt it.

Answer 71

1 question first, what's the little sign after the -b?


On second thought, maybe that's not the best one for me to try.

Answer 72

it is ± (plus or minus)

when you say ±4 you mean "positive or negative 4"

in the formula, it is there to say that the root whatever you get, let say 16, can be either +16 or -16.

Answer 73

Ok. One moment.

Answer 74

So I have -11+/- 5 over 12. Where do I go from there?

Answer 75

yes, so you have

-11 +- 5
--------
12

Answer 76

so either

-11 - 5
--------
12

which gives -4/3 or

-11+ 5
--------
12

which gives 1/2

Answer 77

6x²+11x+4

(2x+1)(3x+4)

Answer 78

-11+5 -6
------- would be ------
12 12

thats not 1/2, is it?

Answer 79

yeah, you caught the err... - 1/2

Now look at the numbers in (one half ) (four thirds)

but it's in a different order in each parenthesis.

Answer 80

(2x+1)(3x+4)

Answer 81

I gtg now -:( I'll be back :)

Answer 82

alright.

Answer 83

http://openstudy.com/users/student_basil#/updates/53542b8be4b066a1cac3b1a0

check it out, and see if you need any of the symbols there... BYE !