Factor x2–19x+88.

Sure, here are the steps to factor the quadratic equation x^2 - 19x + 88:

Step 1: Identify the coefficients of the quadratic equation. In this case, a = 1 (coefficient of x^2), b = -19 (coefficient of x), and c = 88 (constant term).

Step 2: Find two numbers that multiply to give ac (a times c), and add to give b. In this case, ac = 188 = 88, and b = -19. The two numbers that satisfy these conditions are -11 and -8, because -11-8 = 88 and -11 + -8 = -19.

Step 3: Rewrite the middle term of the quadratic equation (the term involving x) as the sum of the terms -11x and -8x. This gives us x^2 - 11x - 8x + 88.

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 - 11x) - (8x - 88).

Step 5: Factor out the greatest common factor from each group. From the first group, we can factor out an x, giving us x(x - 11). From the second group, we can factor out an -8, giving us -8(x - 11).

Step 6: Since the terms in parentheses are the same (x - 11), we can factor out the common binomial term to give the final factored form of the equation: (x - 11)(x - 8).

So, x^2 - 19x + 88 = (x - 11)(x - 8).