How To Factorize Quadratic Equations: Step-By-Step Guide On Factoring X² – 13X + 42

x²-13x+42

(x-6)(X-7)

To factorize the quadratic expression x² – 13x + 42, we can follow these steps:

Step 1: Identify two numbers that multiply to give the constant term (42) and add up to give the coefficient of the middle term (-13).

In this case, the two numbers are -6 and -7. They multiply to give 42 and add up to give -13.

Step 2: Rewrite the middle term (-13x) as the sum of the two numbers found in Step 1, -6x and -7x.

x² – 6x – 7x + 42

Step 3: Group the terms into two pairs and factor out the greatest common factor from each pair.

(x² – 6x) – (7x – 42)
x(x – 6) – 7(x – 6)

Step 4: Factor out the common binomial factor (x – 6).

(x – 6)(x – 7)

Therefore, the quadratic expression x² – 13x + 42 factors to (x – 6)(x – 7).

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