Find a Specific Coefficient in a Product of Binomial/Polynomial Expressions
The question asks to find the coefficient of a specified term in the expansion of a product of two or more binomial or polynomial factors, such as (1+2x^2)(1+x)^4 or (x + y/x)(x+y)^5.
$$\mathrm { P } ( \mathrm { x } ) = ( \mathrm { x } - 1 ) ^ { 4 } + ( \mathrm { x } - 1 ) ^ { 5 }$$ In this polynomial, what is the coefficient of the $x ^ { 3 }$ term? A) 4 B) 6 C) 9 D) 10 E) 11
$$P ( x ) = \left( x ^ { 2 } + 2 \right) ^ { 3 } + ( x - 3 ) ^ { 5 }$$ In this polynomial, what is the coefficient of the $x ^ { 4 }$ term? A) - 9 B) - 3 C) 1 D) 11 E) 21
$$P ( x ) = ( x + 1 ) ^ { 2 } \left( x ^ { 2 } + 1 \right) ^ { 4 }$$ What is the coefficient of the $x ^ { 4 }$ term in the polynomial? A) 8 B) 10 C) 12 D) 14 E) 16