Use synthetic division to simplify. (x^3 + x^2-10x+8) / (x-2)

Question

Use synthetic division to simplify.  (x^3 + x^2-10x+8) / (x-2)

anonymous · Answer

it is really really hard to write synthetic division here, but i can try

anonymous · Answer

list the coefficients of $x^3+x^2-10x+8$ which are 
    1       1     -10     8

anonymous · Answer

okay, I am following you.

anonymous · Answer

then since you are dividing by $x-2$ put a 2 on the side (not a -2)

    1      1      -10     8
2
________________

anonymous · Answer

Okay.

anonymous · Answer

now your answer will be on the bottom line
bring down the 1 
    1      1      -10     8
2
________________
     1

anonymous · Answer

then 1 times 2  is 2 
    1      1      -10     8
2          2
________________
     1

anonymous · Answer

$1+2=3$
    1      1      -10     8
2          2
________________
     1    3

anonymous · Answer

then $3\times 2=6$
    1      1      -10     8
2          2        6
________________
     1     3

anonymous · Answer

Oh, okay.  So you just multiply it by two and then add it in this problem?

anonymous · Answer

yeah you multiply what you get on the bottom row by what is on the side

anonymous · Answer

then add 
see if you can continue

anonymous · Answer

Okay.  I think I get it.  Is the answer x=0?

anonymous · Answer

the answer is not $x=\text{anything}$ you are dividing a polynomial of degree 3 by a polynomial of degree 1
the answer is a polynomial of degree 2, with possibly a remainder

anonymous · Answer

the remainder in this case is zero, you are correct about that
the polynomial of degree two you read of from the coefficients on the bottom row

anonymous · Answer

Okay, so is it going to be something like x^3+3x^2-4x

anonymous · Answer

no no careful

anonymous · Answer

what is the bottom row?

anonymous · Answer

1  3  -4  0

anonymous · Answer

ok now
a polyomial of degree 3 divided by a polynomial of degree 1 gives a polynomial of degree 2

anonymous · Answer

the coefficients are $1,3,-4$

anonymous · Answer

0 is the remainder

anonymous · Answer

Oh, okay.  So is it x^2+3x-4

anonymous · Answer

yes it is

anonymous · Answer

now i have a question

anonymous · Answer

What is your question?

anonymous · Answer

what kind of harp do you play?

anonymous · Answer

I play a lever harp.  It's brand is a Salvi-Anna.  Do you play an instrument?

anonymous · Answer

no 
not for a long time
just curious, so few people play a harp

anonymous · Answer

Yeah, not many people play the harp.  Thank you for you help with my question!

anonymous · Answer

yw