SOLUTION: Without expanding, find the coefficient of x^3 in the normal form of each polynomial. 1. (3x^3+2x^2+5x+1)(x^2-3) 2. (x+1)^5

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Without expanding, find the coefficient of x^3 in the normal form of each polynomial. 1. (3x^3+2x^2+5x+1)(x^2-3) 2. (x+1)^5      Log On


   

Question 1177627: Without expanding, find the coefficient of x^3 in the normal form of
each polynomial.
1. (3x^3+2x^2+5x+1)(x^2-3)
2. (x+1)^5
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

1.
%283x%5E3%2B2x%5E2%2B5x%2B1%29%28x%5E2-3%29
multiply 3x%5E3%2A%28-3%29 and 5x%2Ax%5E2 =>-9x%5E3%2B5x%5E3=-4x%5E3
2.
%28x%2B1%29%5E5 .....use binomial theorem
5C2%2Ax%5E%285-2%29%2A1%5E%285-2%29=10x%5E3