Question

find the remainder x³ -ax² +6x
is devided by x-a ,using
remainder
theorem

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Answer 1

Answer:Let f(x) be x³ - px² + 6x - p.

x - p = 0

x = p

So substitute p into f(x).

Let f(p) be p³ - p(p²) + 6p - p

= p³ - p³ + 6p - p

= 6p - p

= 5p

Therefore 5p is the remainder.

Explanation:We are given to find the remainder when the following polynomial is divided by (x - p) :

Remainder theorem :  When a polynomial p(x) is divided by the factor (x - a), then the remainder is given by p(a).

So, when f(x) is divided by (x - p), the remainder will be f(p).

Therefore, the required remainder is given by

Thus, the required remainder is 5p.