Factorx2+11x+18

Sure, here is the step-by-step solution to factor the quadratic equation x^2 + 11x + 18:

Step 1: Identify the coefficients of the quadratic equation. In this case, a = 1 (coefficient of x^2), b = 11 (coefficient of x), and c = 18 (constant term).

Step 2: Find two numbers that multiply to give ac (a times c), and add to give b. In this case, ac = 118 = 18 and b = 11. The numbers that satisfy this are 9 and 2 because 92 = 18 and 9+2 = 11.

Step 3: Rewrite the middle term (bx) of the quadratic equation as the sum of the terms 9x and 2x. This gives us x^2 + 9x + 2x + 18.

Step 4: Factor by grouping. The first two terms can be grouped together, and the last two terms can be grouped together. This gives us (x^2 + 9x) + (2x + 18).

Step 5: Factor out the greatest common factor (GCF) from each group. The GCF of x^2 and 9x is x, and the GCF of 2x and 18 is 2. This gives us x(x + 9) + 2(x + 9).

Step 6: Notice that (x + 9) is a common factor. Factor out (x + 9), which gives us (x + 9)(x + 2).

So, the factored form of the equation x^2 + 11x + 18 is (x + 9)(x + 2).