Question

Show that (x-1) is a factor of x^3-7*x^2+14*x-8
Hence completely factorize the given expression.

Answer 1

x-1=0
x=1
now, p(x) =x^3-7x^2+14x-8
p(1) =1^3-7*1^2+14-8
1-7+14-8
-6+14-8
8-8
=0
therefore (x-1) is a factor.

hope it will help u. plz mark it as brainlist plz.

Answer 2

={x}^{2}(x-1)-6x(x-1)+8(x-1)
=(x-1)({x}^{2}-6x+8)
=(x-1)[{x}^{2}-4x+2x+8]
=(x-1)[x(x-4)+2(x-4)]
=(x-1)(x-4)(x+2)