Factorize x² + x - 12 Factor out the HCF of the second group?

To factorize x² + x - 12, we need to find two numbers that multiply to -12 and add up to 1 (the coefficient of x).

The two numbers that satisfy these conditions are 4 and -3.

Therefore, x² + x - 12 can be factorized as (x + 4)(x - 3).

To factor out the Highest Common Factor (HCF) of the second group, we need to find the greatest common factor of the coefficients of x and the constant term. In this case, the coefficients of x are 1 and -1, and the constant term is -12.

The greatest common factor of 1 and -1 is 1, and the greatest common factor of 1 and -12 is 1.

Therefore, the HCF of the second group is 1.

So, x² + x - 12 can be factorized as 1(x + 4)(x - 3).

Factorizing x² x - 12

Step 1: Find the HCF of the coefficients in the second group.
The HCF of -1 and -12 is 1.

Step 2: Factor out the HCF from the second group.
x² + x - 12 = x² + 3x - 2x - 12
= x(x + 3) - 2(x + 3)
= (x + 3)(x - 2)

Therefore, the factorization of x² + x - 12 is (x + 3)(x - 2).