Answer:
To factor the given trinomial $10x^2 + 7x - 12$, we need to find two factors that, when multiplied, give the original trinomial.
The steps to factor this trinomial are as follows:
1. Find two numbers that multiply to give the constant term (-12) and add to give the coefficient of the linear term (7).
2. The two numbers that satisfy these conditions are (4) and (-3).
3. Rewrite the trinomial as $(10x^2 + 4x - 3x - 12)$.
4. Factor out the greatest common factor (GCF) from the first two terms and the last two terms.
5. The GCF of the first two terms is $x$, and the GCF of the last two terms is -3.
6. Factoring, we get: $(x(10x + 4) - 3(x - 4))$.
7. Factoring further, we get: $(x + 4)(10x - 3)$.
Therefore, the correct answer is option A: $(x + 4)(10x - 3)$.
