How do you factor the expression 3x^2 + 7x - 6?

To factor the quadratic expression 3x² + 7x - 6, follow these steps:

Multiply the coefficient of x² (which is 3) by the constant term (which is -6): 3 × -6 = -18.

Find two numbers that multiply to give -18 and add up to 7 (the coefficient of x): We need two numbers that multiply to -18 and add up to 7. These numbers are 9 and -2 because: 9 × -2 = -18 and 9 + (-2) = 7.

Rewrite the middle term (7x) using the two numbers found: 3x² + 7x - 6 becomes 3x² + 9x - 2x - 6.

Group the terms: Group the first two terms together and the last two terms together: (3x² + 9x) - (2x + 6).

Factor out the greatest common factor (GCF) from each group: From the first group, 3x² + 9x, the GCF is 3x. From the second group, -2x - 6, the GCF is -2: 3x(x + 3) - 2(x + 3).

Factor out the common binomial factor (x + 3): Now, the expression becomes: (3x - 2)(x + 3).

So, the factored form of 3x² + 7x - 6 is: (3x - 2)(x + 3).