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If g(−x) = −g(x). When g(x) is divided by x − 3 the remainder is 6. Find the remainder when g(x) is divided by x2 − 9.
1. x
2. 2x
3. 3x
4. 4x

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Best answer
Correct Answer - Option 2 : 2x

Calculation:

g(-x) = -g(x) i.e it is an odd function.

N  = pq + r (N is dividend, p is divisor, q is quotient, r is remainder)

So, g(x) = (x - 3)k + 6  (  (x - 3) is dividend, k is divisor, 6 is remainder)

when g(x) mod x- 9

g(x) = m(x- 9) + ax + b ( as if the degree of divisor is 2 (x2)  ,then remainder will be of lesser degree i.e ax + b )
now at x=3

⇒ g(x) = 3a + b = 6

and x = -3 remainder will be -6

⇒ g(-3) = -3a + b=-6

⇒ 2b = 0

so, b = 0 and a = 2

remainder= ax + b = 2x

If f(x) = f(-x); It is called an even function

If f(x) = -f(-x); It is called an odd function.

Dividend = Divisor × Quotient + Remainder

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