Question

find the reminder when x power 4+x power 3-2xpower2+x+1divided by x-1​

Answer 1

Answer:

Dividend = x⁴+x³-2x²+x+1

Divisor = x-1

x⁴+x³-2x²+x+1(x³+2x²+1x-1)

****x⁴-x³

_________________

******2x³-2x²

******2x³-2x²

_________________

************x+1

************x-1

__________________

**Remainder (2)

Quotient = x³+2x+1

Verification by Remainder Theorem:

Let p(x) = x⁴+x³-2x²+x+1

Let p(x) = x⁴+x³-2x²+x+1If x⁴+x³-2x²+x+1 divided by (x-1) then the remainder is p(1)

Let p(x) = x⁴+x³-2x²+x+1If x⁴+x³-2x²+x+1 divided by (x-1) then the remainder is p(1)Remainder = p(1)

Let p(x) = x⁴+x³-2x²+x+1If x⁴+x³-2x²+x+1 divided by (x-1) then the remainder is p(1)Remainder = p(1)= 1⁴+1³-2(1)²+1+1

Let p(x) = x⁴+x³-2x²+x+1If x⁴+x³-2x²+x+1 divided by (x-1) then the remainder is p(1)Remainder = p(1)= 1⁴+1³-2(1)²+1+1= 1+1-2+1+1

= 2

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