Factor completely.5, x, squared, plus, 11, x, plus, 25x 2 +11x+2

The expression you provided seems to be a bit confusing. However, if you're asking to factor the quadratic equation 5x^2 + 11x + 2, here are the steps:

1. Identify the coefficients of the quadratic equation. In this case, a = 5, b = 11, and c = 2.

2. Find two numbers that multiply to give ac (a times c), and add to give b. In this case, ac = 52 = 10 and b = 11. The numbers 10 and 1 fit these criteria because 101 = 10 and 10+1 = 11.

3. Rewrite the middle term (the term involving x) as the sum of the terms that involve the two numbers found in step 2. This gives us 5x^2 + 10x + x + 2.

4. Factor by grouping. The first two terms can be grouped together, and the last two terms can be grouped together. This gives us 5x(x + 2) + 1(x + 2).

5. Notice that (x + 2) is a common factor of both terms. Factoring out (x + 2) gives us (x + 2)(5x + 1).

So, the factored form of the equation 5x^2 + 11x + 2 is (x + 2)(5x + 1).