Final answer:
To factor the expression 15y^2 + 10y - 40, first look for two numbers that multiply to -600 (product of the coefficient of y^2 and the constant term) and add to 10 (the coefficient of y). After finding these numbers, use factoring by grouping to achieve the factored form 5(y - 2)(3y + 4).
Step-by-step explanation:
To factor the quadratic expression 15y2 + 10y − 40, we need to find two numbers that multiply to give the product of the coefficient of y2 (which is 15) and the constant term (which is -40), and add up to the coefficient of the y term (which is 10). These two numbers are 20 and -3 because (15)(-40) = -600 and 20 + (-3) = 17 (we'll adjust this to our needs shortly).
To implement these two numbers into factoring by grouping, we rewrite the middle term (10y) using 20 and -3. So, the expression becomes:
15y2 + 20y - 3y − 40
Now we group the terms:
(15y2 + 20y) + (-3y − 40)
We factor out the common factors from each group:
5y(3y + 4) - 10(3y + 4)
Now we have a common factor (3y + 4) that we can factor out:
(5y - 10)(3y + 4)
As a final step, we can factor out a 5 from the first binomial to make it simpler:
5(y - 2)(3y + 4).
This is the factored form of the original quadratic expression