Question

Given the polynomial P(x)=3x^4−x^3−8x^2−4x
a. Is 3x + 2 a factor?
b. Find the remaining factors if (3x + 2) is a factor

Answer 1

@sourwing

Answer 2

@Mertsj

Answer 3

You have two choices:
1. Divide the polynomial by 3x+2 and see if the remainder is 0
2. Factor the polynomial.

Answer 4

What is your pleasure, my dear?

Answer 5

divide @Mertsj

Answer 6

Did you do it?

Answer 7

Im not sure how to

Answer 8

I can't show you because the draw function isn't working.

Answer 9

can you type it?

Answer 10

First factor out the x

Answer 11

ok I did @Mertsj

Answer 12

Did you get:
x(3x^3-x^2-8x-4)

Answer 13

yeah

Answer 14

So if 3x+2 is a factor then (3x+2)( )=3x^3-x^2-8x-4

Answer 15

wait what? theres a blank in the middle

Answer 16

I know. That would be the answer to the long division problem. It would have to start with x^2 and end with -2

Answer 17

can you show it to me ?

Answer 18

(3x+2)( x^2 -2 )=3x^3-x^2-8x-4

Answer 19

I can try.

Answer 20

ok

Answer 21

___x^2_-x___-2_________________________
3x+2| 3x^3-x^2-8x-4
3x^3+2x^2
-3x^2-8x
-3x^2-2x
-6x-4
-6x-4

Answer 22

why are there lines?

Answer 23

ok nvm I know why

Answer 24

ok so what do I do now?

Answer 25

Because it is a long division problem

Answer 26

Answer the questions.
Is 3x+2 a factor?

Answer 27

no

Answer 28

its no right?

Answer 29

Why do you say no?

Answer 30

because its not in the answer at the top in long division ?

Answer 31

What is the answer to the long division problem?

Answer 32

x^2-x-2

Answer 33

What is the remainder?

Answer 34

0

Answer 35

Is 4 a factor of 12?

Answer 36

yes

Answer 37

Yes it is because 12 /4 is 3 and the remainder is 0

Answer 38

So use that same reasoning. Is 3x+2 a factor of your polynomial?

Answer 39

yes cause the remainder is 0

Answer 40

right?

Answer 41

Yes so now we know that your polynomial is equal to :
x(3x+2)(x^2-x-2)

Answer 42

so how can I find the remaining factors for part b ?

Answer 43

So now do the second part which is to complete the factoring.

Answer 44

You surely know how to factor a trinomial.
x^2-x-2

Answer 45

factoring of the polynomial right ?

Answer 46

3x^3-x^2-8x-4

Answer 47

3x^3-x^2-8x-4=x(3x+2)(x^2-x-2)

Answer 48

We know those are the factors but the third factor can be factored again. That is your job now...to factor x^2-x-2

Answer 49

thanks @Mertsj

Answer 50

did you get it finished?

Answer 51

yes

Answer 52

Good for you!!

Answer 53

I got (x+1) (x-2)

Answer 54

yes
So
3x^4--x^3-8x^2-4x=x(3x+2)(x+1)(x-2)

Answer 55

And that is what you should write on your paper.

Answer 56

thanks so much!

Answer 57

yw