Question

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

Answer 1

Multiply and combine like terms:

2x·x^2 = 2x^3
2x·x = 2x^2
2x·(−2) = −4x
3·x^2 = 3x^2
3·x = 3x
3·(−2) = −6

Add: 2x^3 + (2x^2+3x^2) + (−4x+3x) − 6 = 2x^3 + 5x^2 − x − 6.

So the correct choice is: 2x^3 + 5x^2 − x − 6.