Pawan Prajapati
Last Activity: 4 Years ago
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.