Factorise the quadratic expression below: 𝑥2−6𝑥+5x 2 −6x+5

Sure, here is the step-by-step solution to factorize the quadratic expression x² - 6x + 5:

Step 1: Identify the coefficients of the quadratic expression. Here, a = 1 (coefficient of x²), b = -6 (coefficient of x), and c = 5 (constant term).

Step 2: We need to find two numbers that multiply to give ac (ac = 15 = 5) and add up to give b (b = -6).

Step 3: The two numbers that satisfy these conditions are -5 and -1 because (-5)*(-1) = 5 and (-5) + (-1) = -6.

Step 4: Rewrite the middle term of the quadratic expression as the sum of the products of x and the two numbers found in step 3. So, x² - 6x + 5 becomes x² - 5x - x + 5.

Step 5: Factor by grouping. The first two terms can be grouped together, and the last two terms can be grouped together. This gives us (x² - 5x) - (x - 5).

Step 6: Factor out the greatest common factor (GCF) from each group. The GCF of x² - 5x is x, and the GCF of x - 5 is 1. So, we get x(x - 5) - 1(x - 5).

Step 7: Notice that (x - 5) is a common factor. So, we can factor out (x - 5), which gives us (x - 5)(x - 1).

So, the factorized form of the quadratic expression x² - 6x + 5 is (x - 5)(x - 1).