Synthetic division

[short mango]

i know how to, i just dont understand why it must x-c or x+c in order to use synthetic division for polynomial

[sand laurel]

let's say you wanna divide p(x) = x⁴+ 2x³ -2x²+9x+1 by x-3.
Notice that we can write p(x) as p(x)= (x⁴ - 3⁴) + 2( x³ - 3³) - 2(x²-3²) + 9( x -3) + 3⁴ + 2•3³+ (-2)•3² + 9•3 +1
And we know that, x^n-y^n is always divisible by x-y . So the remainder is just
3⁴ + 2•3³+ (-2)•3² + 9•3 +1 and this is equal to p(3) by remainder theorem which is true for linear polynomials and not particularly true for higher degree polynomials. But you can do something similar for polynomials of degree greater than 1.
That's what I think idk tho