Factorize 2t2 + t - 15

To factorize 2t² + t - 15, we need to find two binomials that multiply to give us 2t² + t - 15. To do this, we can use the factoring method called "AC method." First, we need to find two numbers whose product is 2(-15) = -30 and whose sum is 1. These numbers are 6 and -5. Next, we replace the middle term t with 6t - 5t: 2t² + 6t - 5t - 15 Then we group the terms: (2t² + 6t) - (5t + 15) We factor out the greatest common factor from each group: 2t(t + 3) - 5(t + 3) We notice that we have a common binomial factor of (t + 3), so we can factor it out: (t + 3)(2t - 5) Therefore, the factored form of 2t² + t - 15 is (t + 3)(2t - 5). So, the correct option is: (t + 3)(2t - 5).