Question

when PX= x3-ax2+x is divided by x-a find remainder

Answer 1

x-a=0
x=a

P(x)=x³-ax²+x
P(a)=(a)³-a(a)²+(a)

Answer=a³-a³+a.

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Answer 2

Concept:

Starting with a polynomial, let's say p(x), the Remainder Theorem is introduced. Here, "p(x)" refers to a polynomial p with x as its variable. Then, in accordance with the theorem, multiply that polynomial, p(x), by a linear factor, x - a, where an is only a number. Here, a lengthy polynomial division yields a polynomial q(x), where q stands for "the quotient polynomial," and r is a polynomial remainder (x). It can be stated as follows:

q(x) + r = p(x)/x-a (x)

Given:

P(x)=x³-ax²+x is divided by x-a

Find:

Find the remainder

Solution:

x-a=0

x=a

P(x)=x³-ax²+x

Using remainder theorem,

P(a)=(a)³-a(a)²+(a)

     =a³-a³+a.

Therefore, remainder  of x³-ax²+x when divided by x-a = a³-a³+a.

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