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

2 Answers
Aug 31, 2017

Answer:

#(x-14)^2#

Explanation:

#"note that "-14xx-14=196" and -14 +(-14)=-28"#

#rArrx^2-28x+196#

#=(x-14)(x-14)#

#=(x-14)^2#

Aug 31, 2017

Answer:

#(x - 14) (x - 14)#

Explanation:

#x^2 - 28x + 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 #-28x# and #+196#

Hence we have #14# as the factor;

#-> +196 = - 14 xx - 14#

#-> -28x = - 14x + (- 14x)#

Hence Imputing in the main equation we have..

#x^2 - 28x + 196#

#x^2 - 14x - 14x + 196#

#(x^2 - 14x) (-14x + 196)#

Extract the common factor!

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

Separating the factors!

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