# How do you write x^2+ 4x+3 in factored form?

Apr 3, 2018

$\left(x + 3\right) \left(x + 1\right)$

#### Explanation:

${x}^{2} + 4 x + 3$ is in the general form ${x}^{2} + b x + c$

which can also be written as
${x}^{2} + \left(\text{sum of roots")x+("product of roots}\right)$

which basically means that you need to find TWO roots that when added together equal to 4 and when multiplied together equal to 3.

So the numbers that make the above statement true are
$x = 1 \mathmr{and} x = 3$

Apr 3, 2018

x²+4x+3=(x+1)(x+3)
x²+4x+3=x²+3x+x+3
$= x \left(x + 3\right) + x + 3$
$= \left(x + 1\right) \left(x + 3\right)$