Question

determine without actual division whether x+1 is a factor of x³+x²+x+1​

Answer 1

Answer:

x + 1 = 0

x = -1

${x}^{3} + {x}^{2} + x + 1$

${( - 1)}^{3} + {( - 1)}^{2} + ( - 1) + 1$

$- 1 + 1 - 1 + 1$

$0 - 1 + 1$

$0$

The remainder is coming zero. So x + 2 is a factor of x^3 + x^2 + x + 1

Hope it helps.