Posted by zach w on .
1)let f(x) be a polynomial function explian how to use the factor theorem to check if (xc) is a factor of F(x)
2) use synthetic division to factor X^22x^29x+18 completly

math urgent urgent urgent 
Reiny,
if f(c) = 0 , then xc is a factor
for f(x) = x^2  2x^2  9x + 18
why do you have two x^2 terms, I will assume the first is x^3
If so, we don't need the factor theorem for this one, grouping is obvious
x^3  2x^2  9x + 18
= x^2(x2)  9(x2)
= (x2)(x^2  9)
= (x2)(x+3)(x3)
if you had not seen this, try x = ±1, ±2 , ±3 , that is factors of 18
f(1) ≠ 0
f(1) ≠ 0
f(2) = 0 , yeahhhh, so x2 is a factor
..
f(3) = 0 , so x3 is a factor
f(3) = 0 , so x+3 is a factor
since we have a cubic, there can only be a maximum of 3 algebraic factors
so as above
(x2)(x+3)(x3)