3. Find the value of k, if :r - 1 is a factor of p(x) in each of the following cases: (i) p(:r) = x2 + % + k (iii) p(:r) = h2 - ./2% + 1 (u) p(x) = 2x2 + kx + ./2 (iv) p(x) = h2 - 3x + k.

(i) If (x - 1) is a factor of p(x). then p(l) = 0. Now, p(l) = 0 1 + 1 + k = 0 k = - 2. (u) If (x - 1) is a factor of p(x), then p(l) = O. Now, p(l) = 0 . = 2 + k + J2 = 0 = k =-(2 + J2 ). (ih) If (x - 1) is a factor of p(x), then p(l) = O. Now, p(l) = 0 => k ..... J2 + 1= 0 = k = J2 - 1. 34 (iv) If (x - 1) is a factor of p(x), then p(l) = 0. Now, p(l) = 0 4. Factorise: => k - 3 + k • O => k •i3