Question

p ( x ) = x1 + x3 - 2x2 + x + 1 by ( x - 1 )

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Answer 1

Remainder Theorem:

If p(x) be any polynomial of degree greater than or equal to 1 and p(x) is divided by the linear polynomial (x-a),then the remainder is p(a).

Here ,

p(x)=x⁴+x³-2x²+x+1,

Now,

p(x) is divided by (x-1) then the remainder is p(1)

p(1) = 1⁴+1³-2(1)²+1+1

= 1+1-2+1+1

= 4-2

= 2

Therefore,

Remainder = 2

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