Reading the Product

In the last section you expanded $\left(x+2\right)\left(x+3\right)$ and got $x^{2}+5x+6$. Look at the two numbers 2 and 3. The middle coefficient 5 is their sum, $2+3$. The constant 6 is their product, $2\cdot 3$. The two cross products make the middle term, and the two last terms make the constant.

To factor $x^{2}+bx+c$, find two numbers $p$ and $q$ with $p+q = b$ and $pq = c$. Then $x^{2}+bx+c = \left(x+p\right)\left(x+q\right)$.

To factor $x^{2}+5x+6$, find two numbers with sum 5 and product 6. The pair is 2 and 3, so the factored form is $\left(x+2\right)\left(x+3\right)$. To check, expand the product and compare it with the original trinomial.