Write the coefficient of $x^{2}$ in the given expression: $1 + 2 x + 3 x^{2} + 4 x^{3}$

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Solution

Coefficient of terms in the polynomials:
The coefficient of polynomials is the number multiplied to the variable.
In the expression, $a x^{3} + b x^{2} + c x + d$ ,
$a$ is the coefficient of $x^{3}$ .
$b$ is the coefficient of $x^{2}$ .
$c$ is the coefficient of $x$ .
$d$ is the coefficient of $x^{0}$ .
The given expression is, $1 + 2 x + 3 x^{2} + 4 x^{3}$
Hence, the coefficient of $x^{2}$ is $3$ .

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Question 54 (iii)

Write the coefficient of $x^{2}$ in the following:

$1 + 2 x + 3 x^{2} + 4 x^{3}$

x^{n}

{(1 - 2 x + 3 x^{2} - 4 x^{3} + . . .)}^{- n}

(1 - 2 x + 3 x^{2} - 4 x^{3} + . . . .

\infty)^{4}

x^{2}

x^{2} - 4 x^{3} + 3 x^{2} - 2 x + 1

x = 1 + i

x^{n}

(1 - 2 x + 3 x^{2} - 4 x^{3} + \dots \dots \infty)^{2}

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