Factor x^2+5x+6 = (x+2) (kx+3)

Step-by-step explanation:

Let simplify x²+5x+6 and then we will compare it to (x+2) (kx+3)

Now,

x²+5x+6

Multiply the coefficient of x² (which is 1) to the constant (which is 6),

So, 1*6=6,

Now, we need to find the factor of 6

3*2=6, then, let add them, 2+3=5

Since the addition gave us the coefficient of x (which is 5)

Then, we can rewrite the expression as

x²+5x+6

x²+3x+2x+6

x (x+3) + 2 (x+3)

(x+3) (x+2)

Comparing this to (x+2) (kx+3)

We notice that

(x+3) = (kx+3)

Then, kx=x

Then, k=1