Answer: (x+2)(x+3)
Explanation:
To factorize an equation, you need to find the factors of the leading coefficient, and the constant. In this case, the leading coefficient is 1 (1x²) and the constant is 6. Let's find the factors of both:
Factors of 1 = 1
Factors of 6 = ±1, ±2, ±3, ±6 (± is positive and negative)
Now, we need to figure our the combination of factors that will add up to 5. There are only two that would work.
-1 and 6
2 and 3
Out of these, only 1 multiplies to 6, which is 2 and 3. (-1·6=-6)
Now we have our numbers (1, 1, 2, 3).
From there lets put them into factored form:
(1x+3)(1x+2) or (1x+2)(1x+3).
Now we can take away the 1's to simplify. And the final answer is (x+3)(x+2)
To check, we need to multiply:
x·x=x²
3·x=3x
x·2=2x
3·2=6
We now have the equation, x²+2x+3x+6
Now combine the like terms and we will get our origanal equation, x²+5x+6
Hope that helped a lot.
:)