Answer :

Let q(x) = x^{3} – px^{2} + 6x – p

As we know by Remainder Theorem,

If a polynomial p(x) is divided by a linear polynomial (x – a) then, the remainder is p(a)

⇒ Remainder of q(x) when divided by x – p is q(p)

q(p) = (p)^{3}– p(p)^{2}+ 6(p) – p

⇒ q(p) = p^{3} – p^{3} + 6p – p

∴ Remainder of x^{3} – px^{2} + 6x – p when divided by x – p is 5p

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