Which of the binomials below is a factor of this trinomial?6x2 - 6x - 72A.x + 2B.x + 4C.x - 4D.x - 2SUBMITarrow_backPREVIOUS

To find out which binomial is a factor of the trinomial, we can use the factoring method. The trinomial is 6x^2 - 6x - 72.

Step 1: Multiply the coefficient of x^2 (which is 6) by the constant term (which is -72) to get -432.

Step 2: Look for two numbers that multiply to -432 (from step 1) and add to -6 (the coefficient of x). Those numbers are -18 and 24.

Step 3: Rewrite the middle term of the trinomial as -18x + 24x. So, the trinomial becomes 6x^2 - 18x + 24x - 72.

Step 4: Factor by grouping. The first two terms can be factored as 6x(x - 3) and the last two terms can be factored as 24(x - 3). So, the trinomial becomes 6x(x - 3) + 24(x - 3).

Step 5: Notice that (x - 3) is a common factor. So, the trinomial can be factored as (x - 3)(6x + 24).

Step 6: Simplify the factors. The factor (6x + 24) can be simplified as 2(3x + 12), which is equivalent to 2(3x + 43), or 2(3x + 42 + 4*1).

So, the binomial x + 4 (option B) is a factor of the trinomial.