Factor completely.6, x, squared, minus, 17, x, minus, 36x 2 −17x−3

The expression you provided seems to have a typo. I believe you meant "6x^2 - 17x - 36". Let's factor this expression completely.

Step 1: Identify the coefficients of the quadratic equation. Here, a = 6, b = -17, and c = -36.

Step 2: Find two numbers that multiply to give ac (a times c), and add to give b. We need two numbers that multiply to -216 (6*-36) and add to -17. These numbers are -18 and 12.

Step 3: Rewrite the middle term of the quadratic equation (the term involving x) as the sum of the terms -18x and 12x. This gives us 6x^2 - 18x + 12x - 36.

Step 4: Factor by grouping. This involves factoring out the greatest common factor from each of the two groups:

6x^2 - 18x becomes 6x(x - 3) 12x - 36 becomes 12(x - 3)

Step 5: Notice that the expressions in parentheses are the same. We can factor out the common binomial term to get the final factored form of the equation: (6x + 12)(x - 3).

So, the expression 6x^2 - 17x - 36 factors completely to (6x + 12)(x - 3).