How do you factor #x^2 + 4x + 3#?
The factors are
We are asked for factorise:
First notice that the function is a quadratic and so will have two factors. Since the coefficient of
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
Hence we see that:
Therefore the factors are
(x + 1)(x + 3)
y = x^2 + 4x + 3
Since a - b + c = 0, use shortcut:
- One real root is (-1) and the factor is (x + 1)
- The other real root is (-c/a = - 3), and the factor is (x + 3)
y = (x + 1)(x + 3)