Question

Divide. Use synthetic division, if possible.

(x^4+6x^3-x^2-5x+1)/(x-2)

(x^3+9x^2-5x+11)/(x^2+2)

Answer 1

\[\frac{(x^4+6x^3-x^2-5x+1)}{(x-2)}\]
First you would want to factor out from the first 2 terms such that x-2 would be left out,
for that we can write
\[6x^3=8x^3-2x^3\]
\[\implies \frac{(x^4-2x^3+8x^3-x^2-5x+1)}{(x-2)}\]
Take out
x cube\[\frac{(x^3(x-2)+8x^3-x^2-5x+1)}{(x-2)}\]
Now try to write
-x^2 as something so that when u take out 8x^2 common from 8x^3 and -x^2 you would be left with x-2 just like we did with first 2 terms

Answer 2

Isn't synthetic division where you only use the coefficients? i guess im having more trouble doing with the second one-dividing the x^2+2

Answer 3

I don't know what's "synthetic" division, but u can also simply just divide it, but I prefer to take out factors like that, I find it simpler

Answer 4

Have u done the first one?

Answer 5

you know it would be so much easier to do it on calcilator

Answer 6

i think synthetic division is the one where you have the divisor boxed in the top left

Answer 7

i forget if u box a positive 2 or a negative 2

Answer 8

Like this?