Factor polynomial $$ x^{2}-14x+49 $$
Answer
$$ x^{2}-14x+49 = ( x-7 )^{ 2 } $$
Explanation
Both the first and third terms are perfect squares.
$$ x^2 = \left( \color{blue}{ x } \right)^2 ~~ \text{and} ~~ 49 = \left( \color{red}{ 7 } \right)^2 $$The middle term ( $ -14x $ ) is two times the product of the terms that are squared.
$$ -14x = - 2 \cdot \color{blue}{x} \cdot \color{red}{7} $$We can conclude that the polynomial $ x^{2}-14x+49 $ is a perfect square trinomial, so we will use the formula below.
$$ A^2 - 2AB + B^2 = (A - B)^2 $$In this example we have $ \color{blue}{ A = x } $ and $ \color{red}{ B = 7 } $ so,
$$ x^{2}-14x+49 = ( \color{blue}{ x } - \color{red}{ 7 } )^2 $$This page was created using
Polynomial Factoring Calculator