Final answer:
The first step in factoring the quadratic expression x² -10x-24 is to find two numbers that multiply to -24 and add up to -10, which are -12 and +2, resulting in the factors (x - 12)(x + 2).
Step-by-step explanation:
The student, Tricia, wants to rewrite the quadratic expression x² -10x-24 as a product of polynomials by factoring. The first step in factoring this expression is to find two numbers that multiply to -24 (the constant term) and add up to -10 (the coefficient of the middle term). In this case, the numbers are -12 and +2 because (-12) * (+2) = -24 and (-12) + (+2) = -10. Therefore, her first step would be to express the quadratic as (x - 12)(x + 2), which are the factors of the given quadratic expression.