Question

Using factor theoram show that (x+1) is a factor of x^2+2x+1​.

PLEASE TELL JALDI

Answer 1

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

The zero of the polynomial x + 1 is given by

$x + 1 = 0$

$\implies \: x = - 1$

Let

$f(x) = x² + 2x + 1$

Now by the Remainder Theorem the required Remainder is

$f( - 1) = {( - 1)}^{2} + 2 \times ( - 1) + 1 = 1 - 2 + 1 = 0$

$Hence \: (x+1) \: is \: a \: factor \: of \: x^2+2x+1$