Question

Can `y=x^2 + 10x + 21` be factored? If so what are the factors ?

Answer 1

Yes.

Explanation:

Yes.

`color(white)(xx)y=x^2+10x+21<=>y=(x+3)(x+7)`

Answer 2

`(x+3)(x+7)`

Explanation:

To look for the factored form of a polynomial, look for the numbers whose product is the final number and whose sum is the middle constant.

The possible pairs of numbers whose product is `21` are:

`1,21`

`3,7`

The sum of `3` and `7` are `10`, which is the middle term of the polynomial.

Thus, we can factor `x^2+10x+21` into `(x+3)(x+7)`.

A good way to check your work is to redistribute the factored form.

`(x+3)(x+7)=x^2+7x+3x+21=x^2+10x+21`