Need Help with Polynomial Word Problem

Ms. Ponce owns a company that makes specialized race car engines. From 1985 through 2005, the number of engines produced can be modeled by N (x) = 6x^2 - 4x + 4300 where X is number of years since 1985. The average revenue per engine (in dollars) can be modeled by R (x) = 30 x^2 + 70x + 1,000. Write a polynomial T (x) that can be used to model Ms. Ponce’s total revenue. (Hint: Multiply N(x) times R(x) ).


A. 36x^4 + 66x^2 + 1,300

B. 180x^4 + 300x^3 + 14, 720x^2 + 17,000x + 300, 000

C. 180x^4 - 280x^2 + 300, 000

D. 36x^4 + 39x^3 - 580x^2 + 9,700x + 15, 300


NOTE: I'm not sure how to use the formula specified in the problem. I multiplied N (x) and R (x):

(6x^2 - 4x + 4300)( 30 x^2 + 70x + 1,000)

... but keep getting no solution.

T(x) = N(x) • R(x) = (6x^2 - 4x + 4300) (30x^2 + 70x + 1000) = 180x^4 - 120x^3 + 420x^3 - 280x^2 + 12900x^2 + 6000x^2 + 301000x - 4000x + 4300000 = 180x^4 - 300x^3 + 18620x^2 + 297000x + 430000

Close to B but not quite...

= 180x^4 + 420x^3 + 6000x^2 - 120x^3....................

the answer must be B, because the x^3 term simplifies to 300x^3