Factorise the quadratic expression below: 𝑥2+10𝑥−11x 2 +10x−11

Sure, here is the step-by-step solution to factorize the quadratic expression x^2 + 10x - 11:

Step 1: Write down the quadratic expression: x^2 + 10x - 11

Step 2: Identify the coefficients of x^2, x, and the constant term. Here, the coefficients are 1 (for x^2), 10 (for x), and -11 (the constant term).

Step 3: We need to find two numbers that multiply to give the product of the coefficient of x^2 (which is 1) and the constant term (which is -11), and at the same time, these two numbers should add up to give the coefficient of x (which is 10). The two numbers that satisfy these conditions are 11 and -1 because 11*(-1) = -11 and 11 + (-1) = 10.

Step 4: Rewrite the middle term (10x) of the quadratic expression as the sum of the products of x and the two numbers found in step 3. So, x^2 + 10x - 11 becomes x^2 + 11x - x - 11.

Step 5: Factor by grouping. The first two terms can be grouped together, and the last two terms can be grouped together. This gives: x(x + 11) - 1(x + 11).

Step 6: Notice that (x + 11) is a common factor in both terms. Factor out (x + 11), we get: (x + 11)(x - 1).

So, the factorized form of the quadratic expression x^2 + 10x - 11 is (x + 11)(x - 1).