Answer
$2x^{3}+2x^{2}-19x-21$
Work Step by Step
To find the product of $(x+3)$ and $(2x^{2}-4x-7)$, we need to use the distributive property in which each term of the first polynomial is multiplied to each term of the second polynomial.
$(x+3)(2x^{2}-4x-7)$
$=x(2x^{2}-4x-7)+3(2x^{2}-4x-7)$ $=2x^{3}-4x^{2}-7x+6x^{2}-12x-21$
Then, we simplify the resultant expression:
$=2x^{3}-4x^{2}-7x+6x^{2}-12x-21$
$=2x^{3}-4x^{2}+6x^{2}-7x-12x-21$
$=2x^{3}+2x^{2}-19x-21$
