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

shift 4 units up, and 1 unit left.

it will translate f(x) = 3^x to g(x) = 3^(x+1) + 4