Anyone
using the distributive property, marta multiplied the binomial (2x + 3) by the trinomial (x^2 + x – 2) and got the expression below.
(2x)(x^2) + (2x)(x) + (2x)(–2) + (3)(x^2) + (3)(x) + (3)(–2)
which is the simplified product?
a 2x^3+ 6x^2 – x – 6
b 2x^3 + x^2 – x – 6
c 2x^3 + 5x^2 – x – 6
d2x^3 – x^2 – 7x – 6

(2x)(x²) + (2x)(x) + (2x)(–2) + (3)(x²) + (3)(x) + (3)(–2) =
=2x³ + 2x² - 4x + 3x² + 3x - 6 = 2x³ + 5x² - x - 6

Yes; the correct answer is:  [C]:  "  2x³ + 5x² + x – 6 " .

Explanation:

(2x + 3)(x² + x – 2) =

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

2x³ + 2x² – 4x + 3x² + 3x – 6 = ?

Combine the "like terms" "

+2x² + 3x² = + 5x² ;

– 4x + 3x =  + x

and we have:

 " 2x³ + 5x² + x – 6 " ;  which is:  Answer choice:  [C] .

The answer is 63.!