Factorise the quadratic expression below: 𝑥2−5𝑥+4x 2 −5x+4

Sure, here is the step-by-step factorization of the quadratic expression:

1. Write down the quadratic expression: x² - 5x + 4

2. Identify the coefficients of the quadratic expression. Here, a = 1 (coefficient of x²), b = -5 (coefficient of x), and c = 4 (constant term).

3. We need to find two numbers that add up to b (which is -5 in this case) and multiply to c (which is 4 in this case). The numbers that satisfy these conditions are -4 and -1 because -4 + -1 = -5 and -4 * -1 = 4.

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

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 - 4) - 1(x - 4).

6. Notice that (x - 4) is a common factor. Factor out (x - 4) to get: (x - 4)(x - 1).

So, the factorized form of the quadratic expression x² - 5x + 4 is (x - 4)(x - 1).