Coefficient

 

 What is the coefficient of x in (x^3 + x^2 + x + 1)(7x^6 + 8x^5 - 4x^4 - 10x^3 + 12x^2 - 2x - 8)?    

 

Every term in the first expression is multiplied by every term in the second expression.    

Determine the terms that, when multiplied together, result in the "x" coefficient product.   

 

(x³ + x² + x + 1)(7x⁶ + 8x⁵ – 4x⁴ – 10x³ + 12x² – 2x – 8)    gives you   – 2x    

 

(x³ + x² + x + 1)(7x⁶ + 8x⁵ – 4x⁴ – 10x³ + 12x² – 2x – 8)    gives you   – 8x    

 

                              add them together for the final value                      – 10x