Factor completely.4, x, squared, plus, 39, x, plus, 274x 2 +39x+27

The expression you provided seems to have a typo. It should probably be "4x^2 + 39x + 27". Let's factor this quadratic equation.

The quadratic equation is in the form ax^2 + bx + c. Here, a = 4, b = 39, and c = 27.

We need to find two numbers that multiply to (a*c) = 108 and add up to b = 39.

Those two numbers are 36 and 3 because 36*3 = 108 and 36 + 3 = 39.

We rewrite the middle term of the equation as the sum of the terms 36x and 3x.

So, the equation 4x^2 + 39x + 27 becomes 4x^2 + 36x + 3x + 27.

Now, we factor by grouping. The first two terms have a common factor of 4x, and the last two terms have a common factor of 3.

This gives us: 4x(x + 9) + 3(x + 9).

Now, you can see that (x + 9) is a common factor.

So, the completely factored form of the equation is: (4x + 3)(x + 9).