To factorize x squared plus 5x plus 6, we look for two numbers whose product is 6 and whose sum is 5. These numbers are 2 and 3.
So, we can rewrite the expression as:
x squared plus 5x plus 6 equals x squared plus 2x plus 3x plus 6.
Now, we group the terms and factor by grouping:
x squared plus 2x plus 3x plus 6 equals x times (x plus 2) plus 3 times (x plus 2).
Notice that we have a common factor of x plus 2 in both terms:
x times (x plus 2) plus 3 times (x plus 2) equals (x plus 2) times (x plus 3).
Therefore, the factorized form of x^+5x+6 is (x+2)*(x+3).
