How do you factor x^2-28x+196?

Aug 31, 2017

${\left(x - 14\right)}^{2}$

Explanation:

$\text{note that "-14xx-14=196" and -14 +(-14)=-28}$

$\Rightarrow {x}^{2} - 28 x + 196$

$= \left(x - 14\right) \left(x - 14\right)$

$= {\left(x - 14\right)}^{2}$

Aug 31, 2017

$\left(x - 14\right) \left(x - 14\right)$

Explanation:

${x}^{2} - 28 x + 196$

This is a quadratic equation, hence there are 2 factors..

When finding factors, you need to have two numbers, that will multiply themselves to give the constant and then add or subtract themselves to give the coefficient of $x$..

What am referring to is $- 28 x$ and $+ 196$

Hence we have $14$ as the factor;

$\to + 196 = - 14 \times - 14$

$\to - 28 x = - 14 x + \left(- 14 x\right)$

Hence Imputing in the main equation we have..

${x}^{2} - 28 x + 196$

${x}^{2} - 14 x - 14 x + 196$

$\left({x}^{2} - 14 x\right) \left(- 14 x + 196\right)$

Extract the common factor!

$\textcolor{b l u e}{x} \left(x - 14\right) \textcolor{b l u e}{- 14} \left(x - 14\right)$

Separating the factors!

(x - 14) color(blue)((x - 14)