Factor completely: 3x squared-15x-72.
A-> 3(x squared-5x-24)
B-> (3x-24)(x+3)
C-> 3(x+8)(x-3)
D-> 3(x-8)(x+3)
I got D. But could it be B?
Since it says "factor completely", I think you are correct with D.
Instructions say "factor completely," so I would pick "D."
To factor the expression 3x^2 - 15x - 72 completely, we need to find two binomial factors that multiply together to yield the original expression.
One way to approach factoring is by using the method known as factoring by grouping. Here's how you can do it:
1. Write down the original expression: 3x^2 - 15x - 72.
2. Look for any common factors among the terms. In this case, the terms have a common factor of 3. You can factor out 3 from each term:
3(x^2 - 5x - 24).
3. Now, we need to focus on factoring the quadratic trinomial x^2 - 5x - 24.
4. We are looking for two binomial factors in the form (x + a)(x + b) that multiply together to give us x^2 - 5x - 24. We need to find two numbers (a and b) such that their sum is equal to -5 (coefficient of x) and their product is equal to -24.
5. Therefore, we need to factorize -24 into two numbers that multiply to -24 and add up to -5. After trying different combinations, we find that -8 and 3 satisfy these conditions.
Therefore, the factored form of the quadratic trinomial is:
(x - 8)(x + 3).
6. Finally, since we originally factored out a 3 in step 2, we include it in the factored form as well.
Putting it all together, the complete factored form of 3x^2 - 15x - 72 is:
3(x - 8)(x + 3).
Therefore, the correct choice is C, 3(x + 8)(x - 3). Option B, (3x - 24)(x + 3), is not the correct factored form of the expression.