Question

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

Answer 1

`(x-14)^2`

Explanation:

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

`rArrx^2-28x+196`

`=(x-14)(x-14)`

`=(x-14)^2`

Answer 2

`(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)`