What is the product of the polynomials below? (3x3 + 9x)(x2 - 2) a. 3x5 + 3x3 - 18x b. 3x5 + 3x3 + 18 c. 3x5 - 6x3 + 9x2 - 18x d. 3x5 + 15x2 - 18x

The correct answer is:  [A]:  " 3x⁵  + 3x³ − 18x " .

Explanation:

Given: 


→  " (3x³ + 9x) (x² − 2) " ;   Find this product.

Note:

(a + b) (c + d) = ac + ad + bc + bd ;

→ As such:

→ " (3x³ + 9x) (x² − 2) "  =
 
        (3x³ * x²)  + (3x³ * -2) + (9x * x²) + (9x * -2) = 


→ ( 3x⁽³⁺²⁾ ) + ( - 6x³ ) + ( 9x⁽¹⁺²⁾ )  +  ( -18x) ; 

=  3x⁵ − 6x³ + 9x³ − 18x ; 

Combine the "like terms" ; 

− 6x³ + 9x³ =  + 3x³  ;

And rewrite:


 →  "  3x⁵  + 3x³ − 18x " ; 

 →  which is:  "Answer choice:  [A]:  " 3x⁵  + 3x³ − 18x " .