If x-c is a factor of the polynomial f(x) then c is the root of f(x). True or false?

True. If x-c is a factor of f(x), then, according to the definition of a factor, f(x) = g(x)(x-c), where g(x) is some other polynomial of a degree lesser than f(x).


If so, put x = c in the equation f(x) = (x-c)g(x)





On the left side you get f(c). On the right side,





(c-c)g(c) = 0*g(c) = 0.





Then, according to the equation, f(c) = 0.


And that means, according to the definition of a root of a polynomial, c is the root of f(x).





Hope this helps.If x-c is a factor of the polynomial f(x) then c is the root of f(x). True or false?
trueIf x-c is a factor of the polynomial f(x) then c is the root of f(x). True or false?
here are 2 VERY good web sites...


http://www.purplemath.com/modules/factrt鈥?/a>


http://www.mathsyear2000.org/alevel/pure鈥?/a>