Factorx2−15x+54

Sure, here is the step-by-step solution to factor the quadratic equation x^2 - 15x + 54:

Step 1: Identify the coefficients of the quadratic equation. In this case, a = 1 (coefficient of x^2), b = -15 (coefficient of x), and c = 54 (constant term).

Step 2: Find two numbers that multiply to give ac (a times c), and add to give b. In this case, ac = 154 = 54 and b = -15. The numbers that satisfy this are -9 and -6, because -9-6 = 54 and -9 + -6 = -15.

Step 3: Rewrite the middle term of the quadratic equation as the sum of the terms -9x and -6x. This gives us: x^2 - 9x - 6x + 54.

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) - (6x - 54).

Step 5: Factor out the greatest common factor from each group. From the first group, we can factor out an x, and from the second group, we can factor out a -6. This gives us: x(x - 9) - 6(x - 9).

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

So, the factored form of the equation x^2 - 15x + 54 is (x - 9)(x - 6).