Question

$x^3+x^2+x+1$ is a factor of which of the following polynomial ?

• A. x⁴ - 1
• B. x⁴ + 1
• C. x⁴ - x³ + x² - x
• D. x⁴ - x³ + x² - x + 1

Answer 1

Answer:

A. x⁴ - 1

$x3+x^2+x+1$

$x^2[x+1]+x+1$

$(x+1)[x^2+1]$

$x+1=0$

$x=-1$

$x^4 - 1= (-1)^4-1=+1-1=0$