Factor.x, squared, plus, 7, x, minus, 8x 2 +7x−8

The given expression is x^2 + 7x - 8. Here are the steps to factorize it:

Step 1: Identify the coefficients of the quadratic equation. Here, a = 1 (coefficient of x^2), b = 7 (coefficient of x), and c = -8 (constant term).

Step 2: Find two numbers that multiply to give ac (a times c), and add to give b. In this case, ac = 1*-8 = -8 and b = 7. The numbers that satisfy this are 8 and -1 because 8*-1 = -8 and 8 + -1 = 7.

Step 3: Rewrite the middle term of the quadratic equation as the sum of the terms 8x and -1x. This gives us x^2 + 8x - x - 8.

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(x + 8) - 1(x + 8).

Step 5: Notice that (x + 8) is a common factor. Factor out (x + 8), which gives us (x + 8)(x - 1).

So, the factorized form of the given expression x^2 + 7x - 8 is (x + 8)(x - 1).