It is given that P is a non-zero polynomial such that, P(1+x)=P(1−x) On differentiating both sides w.r.t. x, we get P′(1+x)=−P′(1−x) Now on putting x=0, we get P′(1)=−P′(1) ⇒‌‌P′(1)=0 i.e the polynomial P touches the X-axis at x=1 and P(1)=0( given ) ∴‌‌P(x)=(x−1)2Q(x) ∴ Largest integral value of ' m ' such that (x−1)m divides P(x) is 2.