Question

Use factor theorem to determine if (x - 1) is a
factor of x⁶-x⁵+x⁴-x³+x²+1​

Answer 1

x-1 = 0

so x = 1

p(x) = x⁶-x⁵+x⁴-x³+x²+1

putting x =1 we get

p(1) = 1 - 1 + 1 - 1 + 1 + 1 = 2

so (x - 1) is not a

factor of x⁶-x⁵+x⁴-x³+x²+1