#### Question

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

#### Solution 1

Let p(x) = x^{3} – ax^{2} + 6x – a

x - a = 0

∴ x = a

∴ Remainder = (a)^{3} - a(a)^{2} + 6(a) - a

= a^{3} - a^{3} + 6a - a

= 5a

Therefore, the remainder obtained is 5a.

#### Solution 2

By long division,

Therefore, when *x*^{3} − *ax*^{2} + 6*x* − *a *is divided by *x − a*, the remainder obtained is 5*a*.

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#### APPEARS IN

Solution Find the remainder when x^3 – ax^2 + 6x – a is divided by x – a. Concept: Remainder Theorem.