if a polynomial p(x) is divisible by 2 polynomials (x-a) and (x-b) is it necessary that p(x) will be divisible by (x-a)(x-b)?
Is $f(a)\!=\!0\!=\!f(b)\Rightarrow (x\!-\!a)(x\!-\!b)\mid f(x)\,$ true if $\,a=b?\ $ [Double Factor Theorem]