Question

What is the remainder when (2x4 – 3x3 + x2 – 3x – 3) ÷ (x – 2) ?

6

3

–9

–66

Answer 1

There is a shortcut and a long way.
I will first show you the long way then I will show you the shortcut. :)

Answer 2

So we are dividing by x-2
x-2=0 when x=2
so to do synthetic division you set it up like this (and you might need 0 placeholders if you have "terms missing" ,but here we don't have any missing....the exponents are 4,3,2,1,0 those are consecutive and it ends with 0 so we are good)
now
we look at the coefficients of the top too (those are the numbers in front of the variable
part)
So we have this:
2| 2 -3 1 -3 -3
|
==========================
|

Answer 3

2| 2 -3 1 -3 -3
|
==========================
2 |

Answer 4

I bring down the 2 that is the first step (I brought the first coefficient down of the top)

Answer 5

now take that that 2 and multiply it be that other 2
2| 2 -3 1 -3 -3
| 4
==========================
2 |

Answer 6

add -3 and 4
2| 2 -3 1 -3 -3
| 4
==========================
2 1 |

Answer 7

now whatever those numbers you get when you add you will multiply by that 2 on the outside

Answer 8

so we do 2 times 1
2| 2 -3 1 -3 -3
| 4 2
==========================
2 1 |

Answer 9

so what do I do with that 1 and 2?

Answer 10

kingj, do you know?

Answer 11

so what would the answer be?

Answer 12

I don't give just answers and you should be wanting more than the answer anyways :)
It will be fun and helpful for the exam to know

Answer 13

2| 2 -3 1 -3 -3
| 4 2
==========================
2 1 |
So this is where I left you
See if you can fill in the remaining blanks

Answer 14

I will check