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# How do you factor x^2 + 4x + 3?

Jul 14, 2016

The factors are $\left(x + 3\right)$ and $\left(x + 1\right)$

#### Explanation:

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

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: $\left(x + a\right) \left(x + b\right)$ 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: ${x}^{2} + 4 x + 3$ = $\left(x + 3\right) \left(x + 1\right)$

Therefore the factors are $\left(x + 3\right)$ and $\left(x + 1\right)$

Jul 14, 2016