Question

Which expression represents x2−12x+36 in factored form? (x−4)(x−9) (x+6)2 (x+6)(x−6) (x−6)2

Answer 1

Two factors of x²-12x+36 are

(x-6) and (x-6)

Solution;

x²-12x +36

x²-6x -6x +36 ( split -12x in two parts such that if add them we will get-12x and if multiply will get 36x²)

Taking x common from first two terms and 6 from next two terms

x(x-6) -6(x -6)

taking (x-6) common

(x-6)(x-6)

Answer 2

`x^2 - 12x + 36 = (x-6)(x-6) = (x-6)^2`

Explanation:

We are given the following expression:

`x^2 - 12x + 36`

We need to factor the given expression.

We will do this with the help of technique of splitting the middle term.

Factorization can be done as:

`x^2-12x + 36\\=x^2 - 6x-6x+36\\=x(x-6)-6(x-6)\\=(x-6)(x-6)\\=(x-6)^2`

Thus, the factored form of given expression is:

`x^2 - 12x + 36 = (x-6)(x-6) = (x-6)^2`