Question

Factor the following expression completely.

3x²-30x-72
(A) 3(x−6)(x+4)
(B) 3(x+6)(x−4)
(C) 3(x+4)(x−6)
(D) 3(x−4)(x+6)

Answer 1

To factor 3x²-30x-72 completely, the expression can be simplified to x²-10x-24. Factoring this expression gives A) 3(x-12)(x+2).

Step-by-step explanation:

To factor the expression 3x²-30x-72, we can first find the greatest common factor (GCF) of the three terms, which is 3. We can then divide each term by 3 to simplify the expression. This gives us x²-10x-24.

To factor x²-10x-24, we need to find two numbers that multiply to give -24 and add to give -10. The numbers -12 and 2 satisfy these conditions. Therefore, the factored form of the expression is 3(x-12)(x+2).

So, the correct answer is option (A) 3(x-12)(x+2).