Which is the decomposed form for the expression x^2 + 4x + 3?

It is required to decompose x^2+4x+3.

We shal treat the given expression of secon degree to consist of 2 factors like x+a and x+b. Then the product of the x+a and x+b must be the given expression. So.

(x+a)(x+b) = x^2+4x+3. So,

X^2+(a+b)x+ab = x^2+4x+3. Comparing the coefficients of x^2, x and constant terms on both sides, we get:

1/1 = 4/(a+b) = 3/(ab). Therefore,

a+b =4 and

ab =3.

Solving these inequality, you get, (We do it by guess here without prolonging the procedure): a = 3 and b =1.

Threfore, x^2+4x+3 = (x+3)(x+1)