Question

I'm not asking for the straight forward answer but can someone help me on this world problem please it has 3 parts:
An expression is shown below:

3x3y + 12xy - 9x2y - 36y

Part A: Rewrite the expression so that the GCF is factored completely. Show the steps of your work. (3 points)

Part B: Rewrite the expression completely factored. Show the steps of your work. (4 points)

Answer 1

okay so lets first identify like terms in this function: \(\color{red}{3x^3}\color{blue}{y}+\color{red}{12x}\color{blue}{y}+(\color{red}{-9x^2}\color{blue}{y})+\color{blue}{(-36y)}\)

Answer 2

like terms are 3x^3y, and the -9x^3y @Jhannybean

Answer 3

Not quite there yet! Just hang in there a minute :)

Answer 4

ok

Answer 5

Now between 3 , 12 , 9 and 36 what is the smallest number that is a factor of all the toehr numbers? (hint: you can write out your multiplcation table or divide each number out by the smallest number oyu see)

Answer 6

you*

Answer 7

other*

Answer 8

okay hold on @Jhannybean

Answer 9

Alright :)

Answer 10

its 36 right? @Jhannybean

Answer 11

its 36 right? @Jhannybean

Answer 12

cause 9 x4 = 36 12 x 3 = 36 3 x 12= 36 and 36x 1 = 36

Answer 13

Not quite, between 3, 9, 12 and 36, the GCF is the `prime` number that factors out when we write out the prime factorization. Let's try it out.

between 3, 9, 12, 36 let's test it out. You have:

3: 3 x 1 = 3

9: 3 x 3 = 9

12: 4 x 3 = 2 x 2 x 3

36: 6 x 6 = 2 x 3 x 2 x 3

Looking at all the prime factors, we can see that `3` is common to all these numbers, correct?

Answer 14

ugh this is so hard, i will just guess...

Answer 15

No no, no guessing. Did the previous post confuse you anywhere?

Answer 16

In finding the greatest common factor, we have to simplify our function down to the basic multipliers that are evident throughout the function. We first start by looking at the constants instead of the variables, so prime factorization is what leads us to find that the smallest multiplier between all the numbers would be 3. That means if we were to FACTOR out a multiplier within the function, it would be 3, not 36, because 36 does not multiply with an integer to produce 3.

Answer 17

i thought thats where you find the number that goes into each one of the other numbers (12,3,9- @Jhannybean

Answer 18

i thought thats where you find the number that goes into each one of the other numbers (12,3,9- @Jhannybean

Answer 19

Yup! and 3 is the SMALLEST number that goes into 9, 12 and 36. Do you agree?

Answer 20

oh okay!! i thought it was the greatest number though?

Answer 21

@Jhannybean

Answer 22

The greatest number simplify refers to the LARGEST integer that factors (remember prime factorization!) into all the other numbers. That means when we're factoring all our numbers, what is the number that shows up in all the factorizations? that would be 3!

Do you see what Im saying?

Answer 23

Oh okay i see i see so whats next? @Jhannybean

Answer 24

3: \(\boxed{3}\) x 1 = 3

9: \(\boxed{3}\) x\(\boxed{ 3 }\)= 9

12: 4 x \(\boxed{ 3}\) = 2 x 2 x \(\boxed{3}\)

36: 6 x 6 = 2 x 3 x 2 x \(\boxed{3}\)

Answer 25

Just to make things a bit more clear :)

Answer 26

Okay cool! how did u make that three so bold?

Answer 27

@Jhannybean

Answer 28

`\(\boxed{3}\)`

Answer 29

Huh? @Jhannybean

Answer 30

You were asking how I made it bold, right? I just typed in `\(\boxed{3}\)`

Answer 31

oh okay thats cool ,

Answer 32

well thanks for the help , ill try to do it! @Jhannybean

Answer 33

Anyway, back to what we were solving, i figured it out as well :)

Answer 34

So we have the numerical GCF, and that is `3`.

Now we take another look at the problem and we find are variable thats a GCF.

Answer 35

the COMMON variable in each term of the function? \[3x^3\color{red}{y} + 12x\color{red}{y} - 9x^2\color{red}{y} - 36\color{red}{y}\]

Answer 36

wow ur smart! @Jhannybean

Answer 37

Thanks :) so we factored out 3, what else can we factor out of the function??

Answer 38

Lookat the highlighted red portion @idalisx3_

Answer 39

this is still part a?@Jhannybean

Answer 40

we can factor the x @Jhannybean

Answer 41

i need help with part c i already did part a and part b @Jhannybean

Answer 42

Yes, still part a.

Lets speed things up by solving some steps. Then you can see where I'm going with my explanation.

Our function: \(3x^3\color{red}{y} + 12x\color{red}{y} - 9x^2\color{red}{y} - 36\color{red}{y}\)

This will become \[3y[x^3 +4x-3x^2-12]\]\[3y[x^2(x-3)+4(x-3)]\]\[\boxed{3y[(x^2+4)(x-3)]}\] Is this what you got for part A?

Answer 43

You have not posted a part C so I don't know what you are referring to.

Answer 44

yes i got that and heres part c Part C: If the two middle terms were switched so that the expression became 3x3y - 9x2y + 12xy - 36y, would the factored expression no longer be equivalent to your answer in part B? Explain your reasoning. (3 points)

Answer 45

First of all, is this a quiz question or homework?

Answer 46

quiz question why? @Jhannybean