Question

Factor x3 + x2 + x + 1 by grouping. What is the resulting expression?

Answer 1

Consider the polynomial $x^3 + x^2 + x + 1 .$ You can group first two terms and second two terms in following way:

$x^3 + x^2 + x + 1 =(x^3 + x^2) + (x + 1).$

In first brackets terms $x^3$ and $x^2$ have common factor $x^2$, then

$x^3 + x^2 + x + 1 =(x^3 + x^2) + (x + 1)=x^2(x+1)+(x+1)=(x+1)(x^2+1).$

Answer: $(x+1)(x^2+1).$

Answer 2

X^3 +x^2 +x +1 = x^2(x+1) +x +1 = (x^2 +1)(x +1)

hope helped