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

Dec 13, 2015

Yes.

#### Explanation:

Yes.

$\textcolor{w h i t e}{\times} y = {x}^{2} + 10 x + 21 \iff y = \left(x + 3\right) \left(x + 7\right)$

Dec 13, 2015

$\left(x + 3\right) \left(x + 7\right)$

#### 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 ${x}^{2} + 10 x + 21$ into $\left(x + 3\right) \left(x + 7\right)$.

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

$\left(x + 3\right) \left(x + 7\right) = {x}^{2} + 7 x + 3 x + 21 = {x}^{2} + 10 x + 21$