Final answer:
The quadratic expression 3f^2+2f-5 is factorized by finding two numbers that multiply to -15 and add up to 2, which are 5 and -3. The factorized form is (3f-3)(f+5).
Step-by-step explanation:
To factorize the quadratic expression 3f^2+2f-5 into binomials, we're looking for two numbers that multiply to give us the coefficient of the quadratic term (3) times the constant term (-5), which is -15, and add up to the coefficient of the linear term (2).
After some trial and error, we discover that these two numbers are 5 and -3. Therefore, the correct factors for the expression 3f^2+2f-5 are (3f-3) and (f+5), making our factorized equation:
3f^2+2f-5 = (3f-3)(f+5)