# Polynomials

## Exercise 2.3 Part 2

Question 2: Find the remainder when [x^3 - ax^2 + 6x – a] is divided by x – a.

Alternate Method:

Let, x – a = 0
Hence, x = a
Substituting the value of x in given expression, we get;
x^3 - ax^2 + 6x – a
= a^3 - a(a)^2 + 6a – a
= a^3 - a^3 + 5a= 5a
Thus, 5a is the remainder.

Question 3: Check whether 7 + 3x is a factor of [3x^3 + 7x]

Since, remainder is not zero, hence 7+3x is not a factor of [3x^3 + 7x]

Alternate Method:

Let, 7 + 3x = 0
Or, 3x = 7
Or, x = 7/3
Substituting the value of x in given equation, we get;
3x^3 + 7x
= 3(7/3)^3 + 7 xx (7/3)
= 343/27 + 49/3

Since, remainder is not zero, hence 7+3x is not a factor of [3x^3 + 7x]