Final answer:
The quadratic expression 3x²+10x-8 is factored as (3x-2)(x+4) by finding two numbers that multiply to -24 and add up to 10, and then using factor by grouping.
Step-by-step explanation:
The quadratic expression 3x2+10x−8 can be factored by finding two numbers that multiply to give the product of the coefficient of x2 (which is 3) and the constant term (which is -8), and at the same time add up to the coefficient of x (which is 10).
Let's find the two numbers: they are 12 and -2 because (12)(-2) = -24 (equivalent to 3*(-8)) and 12 + (-2) = 10. Hence, the expression can be rewritten as 3x2+12x-2x−8. Now, we factor by grouping: (3x2+12x) + (-2x-8) = 3x(x+4)-2(x+4), and factoring out the common binomial (x+4), we get (3x-2)(x+4).