Question

Synthetic division help please?(picture below)

Answer 1

please, note that I can write your dividend polynomial as below:
\[x ^{3}-\sqrt{3}x ^{2}+3x-3\sqrt{3}=x ^{2}(x-\sqrt{3})+3(x-\sqrt{3})=...\]

Answer 2

\[...=(x ^{2}+3)(x-\sqrt{3})\]
so?

Answer 3

@Michele_Laino I don't quite understand, can you explain more please?

Answer 4

No clue, so sorrry

Answer 5

I factor out x^2 between the first two terms, namely x^3 and -sqrt(3) x^2,
subsequently I factor out 3, between the third and fourth terms, namely 3x and -3sqrt(3)
at the next step,
I factor out x-sqrt(3) between both terms that yo see at the second equation

Answer 6

@Michele_Laino What's the next step then

Answer 7

please note that you have to perform the division below:
\[\frac{ (x ^{2} +3)(x-\sqrt{3})}{ (x-\sqrt{3}) }=...\]

Answer 8

if we are looking to work the process of synthetic ... the method is quite simple, add and multiply

its the organization of the data that tends to throw people. if you are more comfortable with longhand division, then its usually best to work it from that standpoint.

Answer 9

if we have an nth degree polynomial, then the synthetic division process requires us to have n+1 terms accounted for. thats the only real caveat.

in your case, you have an x^3 so we need 4 terms total ... you have them so nothing is 'missing'

the rest is just organization

Answer 10

@Michele_Laino I got x^2 + 3, which is answer choice B, is that my answer?

Answer 11

Yes! It is, I confirm!

Answer 12

blah blah blah