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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