Using the distributive property, marta multiplied the binomial (2x + 3) by the trinomial (x2 + x – 2) and got the expression below.

(2x)(x2) + (2x)(x) + (2x)(–2) + (3)(x2) + (3)(x) + (3)(–2)

which is the simplified product?

2x3 + 6x2 – x – 6
2x3 + x2 – x – 6
2x3 + 5x2 – x – 6
2x3 – x2 – 7x – 6

2x3 + 5x2 -7x -6 is the answer.

A shortcut to solve this is to look at the answer choices and find the first value that is different. In this case, it is the x2 value. Then, I went to the equation and counted how many x2’s there were. I found there were 2 from (2x)(x) and 3 more from (3)(x2). In total there were 5 x2’s so the correct answer is the one with 5x2.