Question

I don't want an answer, I want to know how to solve this question, and maybe have someone help me complete it.

Explain how you can use the distributive property to check the binomial factors when a trinomial has been factored. Include an example in your explanation.

Answer 1

@triciaal

Answer 2

You are familiar with normal applications of Distributive Property, yes? :)\[\large\rm \color{royalblue}{a}(x+b)=\color{royalblue}{a}x+\color{royalblue}{a}b\]

Answer 3

@zepdrix Yes, I am familiar with the Distributive Property.

Answer 4

Binomials is just an extension of that.\[\large\rm \color{royalblue}{(x+3)}(x-4)=\color{royalblue}{(x+3)}x+\color{royalblue}{(x+3)}(-4)\]

Answer 5

Hopefully the color-coding helps to get the point across.
Instead of distributing something like "a" to each term in the second set of brackets,
I'm distributing an entire set of brackets to each term.

Answer 6

@zepdrix Wait, what did you just do?

Answer 7

Confusing? :d hmm

Answer 8

are you familiar with something known as FOIL?

Answer 9

@RhondaSommer Yeah, I am familiar with FOIL.

Answer 10

\[\large\rm \color{royalblue}{A}(x-4)=\color{royalblue}{A}x+\color{royalblue}{A}(-4)\]This is probably the procedure you're comfortable with,
you're distributing the A to each term in the second set of brackets.
All I'm doing is replacing A with a factor of a polynomial, say (x+3) or something.\[\large\rm \color{royalblue}{(x+3)}(x-4)=\color{royalblue}{(x+3)}x+\color{royalblue}{(x+3)}(-4)\]

Answer 11

No bueno? :o Hmm

Answer 12

I don't understand how A(x - 4) = Ax+A(−4)

Answer 13

probably learned to foil instead of double distribution

Answer 14

Ya you can FOIL if that's easier :)
It seemed like this is what the instructions were asking for though.

Answer 15

A(x+2) = Ax+2A

So you're not familiar with this basic idea of distributing? :o

Answer 16

What are binomial factors and how do you factor trinomials?

Answer 17

that's why i don't like foil... only good for multiplying to binomials...

Answer 18

"two"

Answer 19

x-4 = x + (-4)

Answer 20

@zepdrix Well I kinda understand this A(x+2) = Ax+2A

Answer 21

so it is the exact thing with binomial factors.
(2x+3)(2x+4) will be my example

Answer 22

What exactly does the term binomial factors mean? Sorry if I'm sounding like I don't understand anything.

Answer 23

First=2x * 2x
Outer=2x*4
Inner=3*2x
last=3*4

Answer 24

that is how i would factor it anyway

Answer 25

@RhondaSommer I already understand FOIL.

Answer 26

@RhondaSommer to factor is to find out what was multiplied and to distribute is to multiply, to expand

Answer 27

@zepdrix @triciaal How does one factor a trinomial? Is there some kind of FOIL thing for that?

Answer 28

A binomial is `two terms being added together`.
A trinomial is then `three terms being added together`.

Binomial factors are two binomials being multiplied together.

Recall that factors are things being `multiplied together`
a*b=0
Here a and b are factors.

Here is a binomial: x+1
Here is another: x-2

So if we wanted to construct a trinomial from these factors,
we would multiply the binomial factors together and then do some math to expand them out.
(x+1)(x-2)

Answer 29

That's some of the terminology, not as important as the steps though :)

Answer 30

@zepdrix Alright, I think I'm starting to understand. Then how does one:

"use the distributive property to check the binomial factors when a trinomial has been factored"

Answer 31

Grr lemme get on my other puter XD
I can't use the draw tool very well on this laptop lol.
One sec, I wanna draw it out.

Answer 32

@zepdrix Alright that's fine, take your time.

Answer 33

a trinomial means you have 3 terms
when you have a binomial and you expand the 2 middle terms are like terms so they are added together

Answer 34

Here is a claim that I'm making.