Question

Determine if x^4+x^3+x^2+x+1 has(x+1) a factor

Answer 1

Explanation:

p(x) = x^4 + x³ + x² + x + 1

g(x) = x + 1

x + 1 = 0

x = -1

put x in p(x&

p(-1) = (-1)^4 + (-1)³ + (-1)² + (-1) + 1

= 1 + (-1) + 1 - 1 + 1

= 1 - 1 + 1 - 1 + 1

= 3 - 2

= 1

p(-1) ≠ 0

so x + 1 is not a factor of p(x)