Question

Factor completely x2 − 10x + 25.

(x − 5)(x − 5)
(x + 5)(x + 5)
(x + 5)(x − 5)
(x − 25)(x − 1)

Answer 1

Choice A is the answer.

Explanation:

We have given an quadratic expression.

x² − 10x + 25

We have to find factors of given expression.

Splitting the middle term of the given expression so that the sum of two terms should be -10 and their product be 25.

x²-5x-5x+25

Making groups and taking common, we have

x(x-5)-5(x-5)

Taking x-5 as common, we have

(x-5)(x-5)

Hence,the factors of given expression are x-5 and x-5.

Answer 2

Hence, the factorization o the given algebraic expression:

`x^2-10x+25` is:

`(x-5)(x-5)`

Explanation:

To factor an algebraic equation means to represent it in the most simplest form of the factors.

We have to factor the algebraic equation:

`x^2-10x+25`

We will use the method of splitting the middle term to factor the given algebraic equation.

We could also write the given algebraic equation as:

`x^2-10x+25=x^2-5x-5x+25`

⇒
`x^2-10x+25=x(x-5)-5(x-5)\\\\x^2-10x+25=(x-5)(x-5)`

Hence, the factorization o the given algebraic expression:

`x^2-10x+25` is:

`(x-5)(x-5)`