Q2 of 86 Page 42

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

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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