Question

Is 'x + 1' the factor of; x³+ x²+ x + 1​

Answer 1

Step-by-step explanation:

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Answer 2

let $f(x) = {x}^{3} + {x}^{2} + x + 1$

and, $g(x) = x + 1$

For g(x) to be a factor of f(x) , the following thing must come true : $\boxed{ \tt \: f( - 1) = 0 \: }$

Let's check !

$\quad \: f( - 1) \\ \\ = {( - 1)}^{3} + {( - 1)}^{2} + ( - 1) + 1 \\ \\ = - 1 + 1 - 1 + 1 \\ \\ = (1 - 1) + (1 - 1) \\ \\ = 0 + 0 \\ \\ = 0$
Thus, f( - 1) = 0

Hence, g ( x ) is a factor of f ( x ).