# How do you factor completely: x^2 + 5x + 6?

Mar 13, 2018

$\left(x + 3\right) \left(x + 2\right)$

#### Explanation:

You need to first find 2 number which multiply to make 6 and add to make 5. It is easiest to list the factor pairs of 6:
$6 = 1 \times 6$
$6 = 2 \times 3$

$1 + 6 = 7$
$2 + 3 = 5$

Therefore we use the numbers 2 and 3. it doesnt matter which way round they go in the brackets.

Mar 13, 2018

$\left(x + 2\right) \left(x + 3\right)$, if $y = 0$, $x = - 2$ or $- 3$

#### Explanation:

First, we need to find factors of 6. The factors of 6 are 1,2,3, and 6.
Now see the function. ${x}^{2} + 5 x + 6$. Because there is no substract operation,
$\left(x + a\right) \left(x + b\right) = {x}^{2} + 5 x + 6$
$b x + a x = 5 x ,$ and $a b = 6$
$x \left(b + a\right) = 5 x$, so $b + a = 5$
$a + b = 5$ and $a b = 6$.
Look at the factors. a must be 2 or 3, let's say a is 2, and b must be 3.
So: $\left(x + 2\right) \left(x + 3\right) = 0$, (to find the factor)
$x + 2 = 0 , x = - 2$ ...(1)
$x + 3 = 0 , x = - 3$ ... (2)