Let denote the set of all real numbers

MATHEMATICS · Single correct · A Level · Mathematics · Sequences and series · Sequences and series

Problem

Let

\mathbb{R}

denote the set of all real numbers. Let

a_i, b_i \in \mathbb{R}

for

i \in \{1, 2, 3\}

. Define the functions

f: \mathbb{R} \rightarrow \mathbb{R}

g: \mathbb{R} \rightarrow \mathbb{R}

, and

h: \mathbb{R} \rightarrow \mathbb{R}

\begin{aligned} f(x) &= a_1 + 10x + a_2x^2 + a_3x^3 + x^4, \\ g(x) &= b_1 + 3x + b_2x^2 + b_3x^3 + x^4, \\ h(x) &= f(x+1) - g(x+2). \end{aligned}

f(x) \neq g(x)

for every

x \in \mathbb{R}

, then the coefficient of

x^3

h(x)

is (A) 8 (B) 2 (C) -4 (D) -6