Question

In the expresion of (x - 5)^3 the coefficient of x2 is .............................. ​

Answer 1

Given polynomial is 15−3x+2x

2

A coefficient is a multiplicative factor in some term of a polynomial, a series or any expression; it is usually a number, but may be any expression. In the latter case, the variables appearing in the coefficients are often called parameters, and must be clearly distinguished from the other variables.

As per definition 2 is the coefficient of x

2

Answer 2

Answer :

(x - 5)³

Using identity :

(a - b)³ = a³ - b³ - 3ab (a - b)

⇒ (x)³ - (5)³ - 3 * x * 5 ( x - 5 )

⇒ x³ - 125 - 15x ( x - 5 )

⇒ x³ - 125 - 15x² + 75x

⇒ x³ - 15x² + 75x - 125

Here, the coefficient of x² is (-15).