Question

Divide using synthetic division? Please show how you did it. –3x3 + 11x2 – x + 20 by (x – 4).

Answer 1

Given the factor (x-4) you need to make it equal to zero and solve for x. what do you get for x?

Answer 2

Are u there?

Answer 3

Yeah, I'm new to this so bare with me..

Answer 4

x-4=0, find x.

Answer 5

add 4 to both sides right? x=4?

Answer 6

Correct. Now the next step is to look at the dividend or what you are dividing to make sure there are no missing terms. –3x^3 + 11x^2 – x + 20. Are there any missing terms?

Answer 7

I don't think so..

Answer 8

Nope there isn't because you notice the highest degree is x^3. You have a x^2, x^1 and a constant therefore you are not missing a term. But if you were you would put '0' there.

Answer 9

Write out the coefficient of the dividend:

4 ) -3 11 -1 20
Do you understand how I got this?

Answer 10

Not really.

Answer 11

You took out the x terms?

Answer 12

yup kinda, including the sign also. notice for the '-x' there is no number before it. When this occurs you assume the coefficient is 1. in this case -1

Answer 13

Next step is to bring down the 1st coefficient (-3), then multiply it by the divisor (4):

4 ) -3 11 -1 20
-12
-3

Answer 14

So you multiplied -3 and 4 then divided it by 4?

Answer 15

Nope just multiplied 4*(-3) = -12. Then add 11+(-12)?
Then add 11 and -12:
4 ) -3 11 -1 20
-12
-3 -1
Carry out the same process with -1(4)

Answer 16

Can you finish it from here?

Answer 17

I don't understand how you got the -3 under the -12 tho.

Answer 18

1. Whenever you do synthetic division you always bring down the 1st term (-3). Multiply
that term by the divisor (4): -3*4 = -12.
2. Put the answer in the next column, then add the 2 terms together. (11)+(-12)=-1
3. Repeat the process again only this time with the solution you get from the addition: (-1).

Answer 19

4 ) -3 11 -1 20
-12 -4
-3 -1

Can u figure out the rest of the division from here?

Answer 20

I'm supposed to bring down the 20 right? Then make it 20*4+-4?

Answer 21

Nope this is synthetic division you don't bring down a value like you do in long division. Just follow the steps I mentioned above.

Answer 22

Next step is to add: -1+(-4)?

Answer 23

-5+20 then?

Answer 24

Is that what u get from adding -1+(-4)?

Answer 25

-5. Sorry for taking a bit computers slow

Answer 26

So now we have:
4 ) -3 11 -1 20
-12 -4
-3 -1 -5
Next step:
multiply: 4*(-5). Then place the result under the 20. Then add the result to 20.
Do that and tell me what u got

Answer 27

I got 0

Answer 28

Good so now the synthetic division looks like this:
4 ) -3 11 -1 20
-12 -4 -20
-3 -1 -5 0
So now to write our solution. What is x^3/x?

Answer 29

You mean 4*4*4/4 (which is 16) right?

Answer 30

Nope just simplify what i wrote.

Answer 31

Which part am I simplifying?

Answer 32

ok lets do this the first x term in our answer exponent is going to be 1 less than the exponent on the 1st term (x^3).

Answer: -3x^2 - 1x^? What is the next exponent after 2 in descending order?

Answer 33

1?

Answer 34

good. The next term is the constant (-5)
Answer: -3x^2-1x^1-5 = -3x^2-x-5

Answer 35

You are awesome, thanks so much for explaining this to me. :)

Answer 36

Sure no problem. Apply the same steps to any other problem and you should be good.