Q. 23.7( 19 Votes )

Find the remainder when x3 – px2 + 6x – p is divided by x – p.

Answer :

Let q(x) = x3 – px2 + 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) = p3 – p3 + 6p – p

Remainder of x3 – px2 + 6x – p when divided by x – p is 5p

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