In Need Of Math Help!

[lifeguard200]

I have summer work, and it says something about "Trinomials", can anyone show me where i could find how to SOLVE a problem? Anyway, i went to google and it only talks about the definitions.

[Kryptic]

EDIT - There is the basics on Factoring, if you wanna know how to reverse.. you simply multiply the ( )'s together, then you group all like terms and booya! theres Standard form.

 

 

 

With Trinomials, theres:

 

 

 

Standard form - y=ax(squared) + bx + c

 

 

 

X-Intercept form - y=(x+a)(x+B) , a & b = any number

 

 

 

You can switch back and forth between through several methods.

 

 

 

If you would like to go from Standard to X-Intercept (this is hard, Ill try to explain) you need to do this:

 

 

 

Example 1) a = 1 , b = 1 , c = -6

 

 

 

So the equation is - y=x(squared) + x - 6 >>>Are you with me?

 

 

 

To get the leading term of x(squared), each first term is x, therefore:

 

 

 

y = (x )(x )

 

 

 

Then we need to find what else are in the ( ). The product of the last terms must be -6. Possible answers are:

 

 

 

+ 6 and - 1

 

- 6 and +1

 

+ 3 and - 2

 

- 3 and +2

 

 

 

This tells us that our possible answers to this problem will be:

 

 

 

(x+6)(x-1)

 

(x-6)(x+1)

 

(x+3)(x-2)

 

(x-3)(x+2)

 

 

 

Then you need to test, to see which one is the RIGHT answear, each of these pairs to see which will yield the correct middle term when they are added together.

 

 

 

(x + 6)(x - 1) gives middle term 5x.

 

(x - 6)(x + 1) gives middle term -5x.

 

(x + 3)(x - 2) gives middle term +x. YEA!!!!!

 

(x - 3)(x + 2) gives middle term -x.

 

 

 

Therefore the answear is y = (x + 3)(x - 2), in X-intercept form.

 

 

 

THIS WHOLE PROCESS IS CALLED FACTORING!

[lifeguard200]

ok thanks, good thing i found you so fast :thumbsup:

[lifeguard200]

Here is an example of a problem

 

 

 

Factor the Trinomial

 

 

 

X[squared] + 6X+9.

[Foooman]

I can tell you three ways..though it would be hard to explain without pictures, but ill do it if Kryptic misses something.

 

 

 

Factoring.

 

Graphing.

 

and that formula thing. (dont know what its called atm :oops: )

[greenslime89]

Here is an example of a problem

 

 

 

Factor the Trinomial

 

 

 

X[squared] + 6X+9.

 

 

 

(X + 3)squared

 

 

 

Clue - quote me and you'll see the tiny text...

 

 

 

EDIT: Here we go...

 

[lifeguard200]

I can tell you three ways..though it would be hard to explain without pictures, but ill do it if Kryptic misses something.

 

 

 

Factoring.

 

 

 

 

thats the one that i have alot of problems on #-o

[lifeguard200]

Here is an example of a problem

 

 

 

Factor the Trinomial

 

 

 

X[squared] + 6X+9.

 

 

 

(X times 3)squared

 

 

 

umm what? :oops: :-k :-s

[Foooman]

Here is an example of a problem

 

 

 

Factor the Trinomial

 

 

 

X[squared] + 6X+9.

 

 

 

To factor it:

 

 

 

Find what two numbers multiple to get the 3rd term and add to get the 2nd term.

 

 

 

So in this case the two numbers would both be three because:

 

 

 

3 x 3 =9...which is the 3rd term.

 

3 + 3 = 6...which is the 2nd term.

 

 

 

Then you set it up in

 

 

 

(X _ a)(X _ B)..to get:

 

 

 

(x _ 3)(x _ 3)

 

 

 

Since both signs in the trinomial are positive, the signs in the factors will be positive.

 

 

 

(x + 3)(x + 3)

 

 

 

 

 

Sorry if I'm not to good at explaining...I'm in dire need of pencil and paper.

[lifeguard200]

Here is an example of a problem

 

 

 

Factor the Trinomial

 

 

 

X[squared] + 6X+9.

 

 

 

To factor it:

 

 

 

Find what two numbers multiple to get the 3rd term and add to get the 2nd term.

 

 

 

So in this case the two numbers would both be three because:

 

 

 

3 x 3 =9...which is the 3rd term.

 

3 + 3 = 6...which is the 2nd term.

 

 

 

Then you set it up in

 

 

 

(X _ a)(X _ B)..to get:

 

 

 

(x _ 3)(x _ 3)

 

 

 

Since both signs in the trinomial are positive, the signs in the factors will be positive.

 

 

 

(x + 3)(x + 3)

 

 

 

 

 

Sorry if I'm not to good at explaining...I'm in dire need of pencil and paper.

 

 

 

i kinda get what your explaining, so how does the final problem look like? Sorry if it looks like im asking for the answers but i just need like an example to follow. Thanks foooman for the help so far

[ndn3master]

EDIT - There is the basics on Factoring, if you wanna know how to reverse.. you simply multiply the ( )'s together, then you group all like terms and booya! theres Standard form.

 

 

 

With Trinomials, theres:

 

 

 

Standard form - y=ax(squared) + bx + c

 

 

 

X-Intercept form - y=(x+a)(x+B) , a & b = any number

 

 

 

You can switch back and forth between through several methods.

 

 

 

If you would like to go from Standard to X-Intercept (this is hard, Ill try to explain) you need to do this:

 

 

 

Example 1) a = 1 , b = 1 , c = -6

 

 

 

So the equation is - y=x(squared) + x - 6 >>>Are you with me?

 

 

 

To get the leading term of x(squared), each first term is x, therefore:

 

 

 

y = (x )(x )

 

 

 

Then we need to find what else are in the ( ). The product of the last terms must be -6. Possible answers are:

 

 

 

+ 6 and - 1

 

- 6 and +1

 

+ 3 and - 2

 

- 3 and +2

 

 

 

This tells us that our possible answers to this problem will be:

 

 

 

(x+6)(x-1)

 

(x-6)(x+1)

 

(x+3)(x-2)

 

(x-3)(x+2)

 

 

 

Then you need to test, to see which one is the RIGHT answear, each of these pairs to see which will yield the correct middle term when they are added together.

 

 

 

(x + 6)(x - 1) gives middle term 5x.

 

(x - 6)(x + 1) gives middle term -5x.

 

(x + 3)(x - 2) gives middle term +x. YEA!!!!!

 

(x - 3)(x + 2) gives middle term -x.

 

 

 

Therefore the answear is y = (x + 3)(x - 2), in X-intercept form.

 

 

 

THIS WHOLE PROCESS IS CALLED FACTORING!

english pl0x?

[Foooman]

i kinda get what your explaining, so how does the final problem look like? Sorry if it looks like im asking for the answers but i just need like an example to follow. Thanks foooman for the help so far

 

 

 

(x+3)(x+3)

 

 

 

-or-

 

 

 

(x+3){squared}

 

 

 

 

 

Both are correct. and wow Kryptic..thats a lot of typing.

[lifeguard200]

EDIT - There is the basics on Factoring, if you wanna know how to reverse.. you simply multiply the ( )'s together, then you group all like terms and booya! theres Standard form.

 

 

 

With Trinomials, theres:

 

 

 

Standard form - y=ax(squared) + bx + c

 

 

 

X-Intercept form - y=(x+a)(x+B) , a & b = any number

 

 

 

You can switch back and forth between through several methods.

 

 

 

If you would like to go from Standard to X-Intercept (this is hard, Ill try to explain) you need to do this:

 

 

 

Example 1) a = 1 , b = 1 , c = -6

 

 

 

So the equation is - y=x(squared) + x - 6 >>>Are you with me?

 

 

 

To get the leading term of x(squared), each first term is x, therefore:

 

 

 

y = (x )(x )

 

 

 

Then we need to find what else are in the ( ). The product of the last terms must be -6. Possible answers are:

 

 

 

+ 6 and - 1

 

- 6 and +1

 

+ 3 and - 2

 

- 3 and +2

 

 

 

This tells us that our possible answers to this problem will be:

 

 

 

(x+6)(x-1)

 

(x-6)(x+1)

 

(x+3)(x-2)

 

(x-3)(x+2)

 

 

 

Then you need to test, to see which one is the RIGHT answear, each of these pairs to see which will yield the correct middle term when they are added together.

 

 

 

(x + 6)(x - 1) gives middle term 5x.

 

(x - 6)(x + 1) gives middle term -5x.

 

(x + 3)(x - 2) gives middle term +x. YEA!!!!!

 

(x - 3)(x + 2) gives middle term -x.

 

 

 

Therefore the answear is y = (x + 3)(x - 2), in X-intercept form.

 

 

 

THIS WHOLE PROCESS IS CALLED FACTORING!

english pl0x?

 

 

 

im starting to understand it a little more, let me put up another problem with this help and can someone see if im doing it right?

[unknownmasterofnothing]

Trinomials- three different factors

 

can be y=3a+4b+5c

 

 

 

Factoring can be done with a quadratic like

 

y=x^2+7x+10

 

 

 

Theres two steps that can be done.

 

A number ____ times a number ___ equals 10

 

A number ____ plus a _____ equals 7

 

so.. 5*2=10 and 5+2=7

 

 

 

For a cubic function, theres many ways such as using pascal's triangle. You can use long division or other methods.

 

 

 

But basically factoring means pulling out what is in common with all the terms.

 

 

 

Such as 5x+5b. You can take out the 5

 

to get 5 (x+B)

 

 

 

or

 

 

 

4ab+6ab+2ab

 

becomes

 

2ab(2+3+1)

 

2ab(6)

[greenslime89]

Does this help?

 

[Adam007]

Have someone irl teach you it - won't be hard, it's a very common thing to know that most everyone's learned in highschool. It will make a lot more sense because it's very hard to explain anything mathwise online. These guys are doing a great job explaining though - it's pretty hard explaining such abstract things, especially typing it.

[lifeguard200]

Does this help?

 

 

 

 

in a bit, but yea, thanks for the help EVERYONE

[lifeguard200]

Have someone irl teach you it - won't be hard, it's a very common thing to know that most everyone's learned in highschool. It will make a lot more sense because it's very hard to explain anything mathwise online. These guys are doing a great job explaining though - it's pretty hard explaining such abstract things, especially typing it.

 

 

 

only problem adam, people i talked to either forgot it, or dont have the time :lol: , but yes, these intelligent people have the time to help me (which is working) and it really helps me do my summer work now! thanks everyone

 

 

 

a big :thumbsup: to everyone that helped me

[mad4u689]

I came too late to help, but if you have any more problems, just post and the tip.it team will deliver 8-) :D

[lifeguard200]

ok now that i get the X[squared]+6X+9 thing...

 

 

 

there is a new one i dont get.

 

 

 

2X(squared) +x-6,

 

 

 

how do i solve this one?

[Foooman]

ok now that i get the X[squared]+6X+9 thing...

 

 

 

there is a new one i dont get.

 

 

 

2X(squared) +x-6,

 

 

 

how do i solve this one?

 

 

 

NOTE: If you can make the first term just x(squared) you do it like the others:

 

 

 

For Example:

 

2x(square)+4x - 6

 

 

 

is done like:

 

 

 

2( x(squared)+2x -3)

 

 

 

which comes to:

 

 

 

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

 

 

 

2x(squared) + x -6

 

 

 

Lets start with what the answer can look like.

 

 

 

(2x_1)(x_6)

 

(2x_6)(x_1)

 

(2x_3)(x_2)

 

(2x_2)(x_3)

 

 

 

We know that one of the factors has a negative sign in it due to the third term being negative.

 

 

 

So now our options are:

 

 

 

(2x+1)(x-6)

 

(2x+6)(x-1)

 

(2x+3)(x-2)

 

(2x+2)(x-3)

 

(2x-1)(x+6)

 

(2x-6)(x+1)

 

(2x-3)(x+2)

 

(2x-2)(x+3)

 

 

 

Now we must get the middle term for each of these (there is no shortcut that i know of)...

 

 

 

(2x+1)(x-6) - -11 ----- {(2 x-6) +1}

 

(2x+6)(x-1) - 4 ----- {(2 x-1)+6}

 

(2x+3)(x-2) - -1 ----- {( 2 x-2)+3}

 

(2x+2)(x-3) - -4 ----- {(2 x-3)+2}

 

(2x-1)(x+6) - 11 ----- {(2 x 6)+ -1}

 

(2x-6)(x+1) - -4 ----- {(2 x 1)+ -6}

 

(2x-3)(x+2) - 1 ----- {(2 x 2)+ -3}

 

(2x-2)(x+3) - 4 ----- {(2 x 3)+ -2}

 

 

 

Since the middle term is 1...We can conclude:

 

 

 

(2x-3)(x+2) = 2x(squared) + x - 6

[mad4u689]

2x^2 + x - 6

 

 

 

Use the same type of guess and check method :D Only this time, there's something extra you have to keep in mind the coefficient (in this case, 2) in front of the variable (in this case, x - this terminology is good to know, by the way, for the future :D) So to get a 2x^2, what could factors possibly be? (2x)(x) would equal 2x^2, or (x)(2x), but those are the only real possiblities. What factors could be multiplied to get (-6)? (1)(-6), (2)(-3), (3)(-2), (6)(-1), (-1)(6), (-2)(3), (-3)(2), (-6)(1).

 

 

 

So what do you know? You know that if the trinomial 2x^2 + x -6 factors neatly, that the factors will look like this: (2x + __ ) (x +__ ). Now when mutiplying factors like this, you FOIL it (Multiply the First term in each, the Outer terms in each, the Inner terms, and the Last terms). You know that in the end, you are looking for just 1x in the middle.

 

 

 

What combination of the factors of -6 could be put in there to make it all work out neatly? Try guessing and checking until you get the hang of it.

 

 

 

Remember that if you tried the first combination, 1 and -6, you would FOIL it and get: 2x^2 + 1x -6x -6, which equals 2x^2 -5x -6 when simplified. But this isn't what you're looking for! So keep trying, and good luck :)

 

 

 

If you get to more complicated problems, you may find that factoring won't work in every case. Factoring only works when the problem works itself out neatly! There are other more complicated (and less guessing involved) ways to find out, and you'll probably get to that later in your course. :D

[Sp4de]

A way I use is much easier and less paper-consuming.

 

 

 

x^2+6x+9

 

 

 

Find the multiplies of 9 that add up to the middle term, in this case, 6.

 

 

 

A multiple of 9 is 3x3 and 3+3 = 6

 

 

 

So, from there, just put that into brackets.

 

 

 

(x+3)(x+3) which equals into a simpler form of (x+3)^2 [^2 means square]

[Sp4de]

-cough cough-

 

 

 

=weeze=

 

 

 

I fail.

[Foooman]

Sp4de I'm 99% possitive that 2nd one is completely incorrect.