Question

using factor theorem, show that a-b is a factor of a(b²-c²) + b(c²-a²) + c(a²-b²​

Answer 1

Step-by-step explanation:

p(x) = a($b^{2} - c^{2}$) + b($c^{2} -a^{2}$) + c($a^{2} -b^{2}$)

lets check whether p(b) = 0 [factor theorem]

p(b) =$b^{3} -bc^{2} + bc^{2} -b^{3} +cb^{2} -cb^{2}$

• [b^3 and (- b^3) cancels]
• [-ve and +ve bc^2 cancels]
• [-ve and +ve cb^2 cancels]

therefore,

p(b) = 0 + 0 + 0

      = 0

hence (a-b) is a factor of the polynomial.

HOPE THIS HELPS YOU