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Find the remainder when x^3 – ax^2 + 6x – a is divided by x – a. - Mathematics

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Find the remainder when x3 – ax2 + 6x – a is divided by x – a.

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Solution 1

Let p(x) = x3 – ax2 + 6x – a

x - a = 0

∴ x = a

∴ Remainder = (a)3 - a(a)2 + 6(a) - a

                   = a3 - a3 + 6a - a

                   = 5a

Therefore, the remainder obtained is 5a.

Solution 2

By long division,

Therefore, when x3 − ax2 + 6x − is divided by x − a, the remainder obtained is 5a.

Concept: Remainder Theorem
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APPEARS IN

NCERT Class 9 Maths
Chapter 2 Polynomials
Exercise 2.3 | Q 2 | Page 40
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