Final answer:
To factor the expression 15x²-5x-10, we start by factoring out the greatest common factor, which is 5, resulting in 5(3x² - x - 2). Then we factor the quadratic part to get the final factored form: 5(3x + 2)(x - 1).
Step-by-step explanation:
To factor the quadratic expression 15x²-5x-10, we first look for any common factors in each term. We can see that all the terms are divisible by 5. Let's factor out 5 first:
5(3x² - x - 2)
Now, we need to factor the quadratic expression inside the parentheses. We're looking for two numbers that multiply to give us (3)(-2) = -6 and add to give us -1, which are the coefficients in our expression's second term. The numbers that meet these criteria are -3 and 2. Therefore, we can write the factored form as:
5(3x + 2)(x - 1)
We have factored the expression by first taking out the greatest common factor and then factoring the remaining quadratic.