Question

An expression is shown below:

2x3y + 18xy - 10x2y - 90y

Part A: Rewrite the expression so that the GCF is factored completely. (3 points)

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

Part C: If the two middle terms were switched so that the expression became 2x3y - 10x2y + 18xy - 90y, would the factored expression no longer be equivalent to your answer in part B? Explain your reasoning. (3 points)

Answer 1

@BPDlkeme234 @jigglypuff314 @DanJS @imammalik_806 @SolomonZelman

Answer 2

@mathstudent55

Answer 3

@sleepyjess

Answer 4

@inkyvoyd

Answer 5

@Haseeb96 @DullJackel09

Answer 6

@gabbyalicorn @Mchilds15 @mathstudent55

Answer 7

I have no idea. Sorry! @rebeccaxhawaii

Answer 8

@re314 @reemii @Raphandryu @jacobciezki @londoncat @lordhelix8th @pandaecat

Answer 9

@Tiny_Tina @tazzwilliams @theghostlycreeper @IconForHire56 @Ashchu117 @adamlevine @ajolly @studio-games @DullJackel09 @KayHoo22 @londoncat

Answer 10

@xxbatmanevoxx @chris215 @chasebraves @charliemath @bani_xoxo @mathstudent55

Answer 11

Hi i can help

Answer 12

Ok!

Answer 13

I have part a:

2x^3 y + 18 xy −10x^2 y−90y = 2y (x^3 − 5x^2 + 9x − 45)

Answer 14

I think

Answer 15

so now distribute that to check that

Answer 16

?

sorry I have no idea how to do this

Answer 17

so when you distribute it should be\[2x^3y-10x^2y+18xy-90y\]

Answer 18

does that match the original equation?

Answer 19

looks like it does!

Answer 20

Ok Cool thanks.

Answer 21

What about part b though? I don't know how to do that

Answer 22

Now to factor that, you need to factor the x^3-5x^2+9x-45

Answer 23

do you know how to factor?

Answer 24

not really...

Answer 25

okay so i can tell you

Answer 26

Ok

Answer 27

so when you are factoring, you are basically trying to simplify an expression

Answer 28

for example if you wanted to factor x^2+25 you would want to find the factors of x^2 and the factors of 25

Answer 29

you will need to learn how this is used more in geometry

Answer 30

so for this expression, you need to find the factors of each

Answer 31

when you are factoring, it is one of these things where is is a trial and error

Answer 32

Ok.

Answer 33

So how would I factor x^3-5x^2+9x-45 ?

Answer 34

you want to find two expressions that when you FOIL them out, it becomes that expression

Answer 35

do you know FOIL?

Answer 36

i think so...

Answer 37

im not 100% sure how to do it

Answer 38

ok for example, FOIL (x^2+9)(x-5)

Answer 39

we can see then how much you know

Answer 40

i think i know nothing! lol

Answer 41

does that explain it sort of?

Answer 42

that is the concept

Answer 43

ok so First Outer Inner Last

Answer 44

yes

Answer 45

So the First would be x^2 times x

Answer 46

YES

Answer 47

then x^2 times 5

Answer 48

times negative 5

Answer 49

remember the signs

Answer 50

\[(x^2+9)(x-5)= (x^2*x)-(5*x^2)+(9*x)-(9*5)\]

Answer 51

That is what it looks like

Answer 52

oh ok

Answer 53

now multiply everything in parenthesis

Answer 54

-10 + -8x^2 ? i dont know but i get the idea of it

Answer 55

No... so what is x^2*x

Answer 56

x^3

Answer 57

ok so the first part is x^3

Answer 58

what is 5*x^2

Answer 59

5x^2

Answer 60

What about part b though?

Answer 61

I basically just factored it out for you already

Answer 62

that expression factored out is (x^3 − 5x^2 + 9x − 45)

Answer 63

so your part b would be 2y(x2+9)(x−5)

Answer 64

Thanks!!! Can you help me with part c?

Answer 65

sure

Answer 66

it is no because they when factored, they are the same regardless

Answer 67

Thank you so much for your help!!!

Answer 68

No Problemo