L Def.ermine which of the fo Uowing polyrwmUtls hos (.x + I ) a factor: <.i r + r + .x + 1 r -s2 -(2 + J2J.x + J2

If (.x + 1) is a factor of p(z) == z3 + x2 + z + 1, then p(- 1) = 0 Now, p(- 1) = - 1+ 1- 1+ 1 = 0. Hence, (.x + 1) is a factor. (ii) If(.x + 1) is a fiictor of p(.x) = z4 + %' + x:2 + x + 1, then pl.- 1) = 0. Now, p(- 1) = 1- 1 + 1- 1+ 1= 1• 0. Hence, (.x + 1) is not a factor. (ii.i IC + 1) is a factor ofp(-c) = x4 + &3 + 3x2 + x + 1, then p(- 1) = o. Now, p(- 1) • 1- 3 + 3 - 1+ 1 = 1¢ 0. Hence, (x + 1) is not a factor. Pot.YNOMALS 33 (iv) If (x + 1) is a factor of p(:r) = r - x2 - (2 + J2 )% + J2 , then p(- 1) = 0. Now, p(- 1) = (- 1)3 - (- 1)2 -(2 + J2 )(- 1) + J2 = - 1- 1 + 2 + J2 + J2 = 2J2 ¢ 0. Hence, (x + 1) is not a factor.