Ayo synthetic division

Question

Allison · Answer

attachment

Allison · Answer

@Hero @dude

darkknight · Answer

ill do this on paper and upload for u to help, its kinda like long division

Allison · Answer

I got multiple answers, can you see if I'm right? 
I got decimals.

darkknight · Answer

uploading gimme a min

jhonyy9 · Answer

like a first step is good to know when the sum of coeficients of an equation is equal zero so this mean that this equation is divisible by (x-1)

jhonyy9 · Answer

like in this case of your posted equation

f(x) = x^3 +3x^2 -36x +32

the sum of coefficients will be

1 +3 -36 +32 = -36 +36 = 0

so from this result that this equation is divisible by x-1

darkknight · Answer

I will attach a picture to help out with this, Allison you need to learn that synthetic long division is basically long division but with variables too. So you know how when you do something like 85832/7474 you would take 8 and  7 and see how many times 7 can go into 8, and then after that take the remainder and move it over to the next place well synthetic division works the same. 
For example if you have x^3 + 20x^2 -20x + 5
and you want to divide by x-5
then you see that x^3 divided by x = x^2
and then x^2 times -5 = -5x^2
next term over is 20x^2 so we take that and -5x^2 and get 15x^2, now 15x^2-20x and 15x times x = 15x^2 so the next part of our answer is 15x

Allison · Answer

Okay

SemiDefinite · Answer

in it's purest form:

$x^3 + 3 x^2 - 36 x + 32 = (x^2 + 4 x - 32) × (x - 1) + 0$

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