Suppose we want to factorise

x
^{
2
}
+ 7x + 12

We factorise it by splitting the middle term

x
^{
2
}
+ 7x + 12

= x
^{
2
}
+ 4x + 3x + 12

= x(x + 4) + 3(x + 4)

= (x + 3) (x + 4)

So, x
^{
2
}
+ 7x + 12 = (x + 3) (x + 4)

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