Question

Using factor theorem, Show that (a - b) is the factor of a (b2-c2) +b (c2-a2) + c (a2-b2)

Answer 1

Step-by-step explanation:

according to the factor theorem

if x-a is. a factor => put x= a..the

polynomial should become zero.

since (a-b) is a factor

=> putting a= b we have

b(b²-c²)+ b( c²-b²) +c (b²-b²)

= b³-bc²+bc²-b³

= 0

therefore, (a-b) is a factor of the given polynomial

proved.

Answer 2

Answer:

Step-by-step explanation:

we have

a(b^2-c^2)+(c^2-a^2)+c(a^2-b^2)=b(b^2-c^2)+b(c^2-b^2)+c(b^2-b^2)

b^2-bc^2+bc^2-b^3+c(b^2-b^2)=0

hence a-b is a factor of a (b2-c2) +b (c2-a2) + c (a2-b2)