Question

Factorize the following
$x {}^{2} - 2x + 1$
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Answer 1

$HEYA \: \\ \\ GIVEN \: \: QUESTION \: \: Is \: \: \\ \\ x {}^{2} - 2x + 1 = f(x) \\ \\ f(x) = x {}^{2} - x - x + 1 \\ \\ f(x) = x(x - 1) - 1(x - 1) \\ \\ f(x) = (x - 1)(x - 1) \\ \\ so \: \:factors \: of \: \: x {}^{2} - 2x + 1 \: \: \: are \: \: \: \\ (x - 1)(x - 1)$

Answer 2

given :- x² - 2x + 1

using splitting method,

➡ x² - (x + x) + 1

➡ x² - x - x + 1

➡ x (x - 1) - 1(x - 1)

➡ (x - 1) (x - 1)

hence, (x - 1) is the factor of given polynomial.