What are the factors of X^2+4x+3x

The factors are (x+3) and (x+1)

Step by Step Explanation:

We are asked for factorise:
x^2+4x+3

First notice that the function is a quadratic and so will have two factors. Since the coefficient of
x^2 is 1, the factors will be of the form:
(x+a) (x+b)

We will assume that a and b are integers.

Hence, we need to find a and b such that the product of the factors is equal to the given quadratic function.
Now consder the absoute value of constant term, 3. Since 3 is prime its only factors are 3 and 1. Since the constant term is positive, a and b can only be 3 and 1 or -3 and -1.
Finally observe that the coefficient of x is positive 4 and that the sum of 3 and 1 is positive 4. Thus, a and b must be 3 and 1 (or the other way around, but this makes no difference to our factorisation)
Hence we see that:
x^2+4x+3 = (x+3) (x+1)

Therefore the factors are
(x+3) and (x+1)