Question

find the remainder when X raised to power 4 minus 2 power 2 X raise to power 2 + 2 x minus k is divided by x minus k​

Answer 1

When a polynomial f(x) is divided by x2−5 the quotient is x2−2x−3 , and the remainder is zero. What is the polynomial and all its zeroes?

By division theorem,

Dividend=divisor×quotient+ remainder

Dividend=divisor×quotient+ remainderDividend=F(x)

Dividend=divisor×quotient+ remainderDividend=F(x)Divisor=x^2–5

Dividend=divisor×quotient+ remainderDividend=F(x)Divisor=x^2–5Quotient=x^2–2x-3

Dividend=divisor×quotient+ remainderDividend=F(x)Divisor=x^2–5Quotient=x^2–2x-3Remainder=0,then

Dividend=divisor×quotient+ remainderDividend=F(x)Divisor=x^2–5Quotient=x^2–2x-3Remainder=0,thenF(x)=(x^2–5)(x^2–2x-3)

Dividend=divisor×quotient+ remainderDividend=F(x)Divisor=x^2–5Quotient=x^2–2x-3Remainder=0,thenF(x)=(x^2–5)(x^2–2x-3)F(x)=x^4–2x^3–8x^2+10x+15

Dividend=divisor×quotient+ remainderDividend=F(x)Divisor=x^2–5Quotient=x^2–2x-3Remainder=0,thenF(x)=(x^2–5)(x^2–2x-3)F(x)=x^4–2x^3–8x^2+10x+15F(x)=(x-√5)(x+√5)(x-3)(x+1)

Dividend=divisor×quotient+ remainderDividend=F(x)Divisor=x^2–5Quotient=x^2–2x-3Remainder=0,thenF(x)=(x^2–5)(x^2–2x-3)F(x)=x^4–2x^3–8x^2+10x+15F(x)=(x-√5)(x+√5)(x-3)(x+1)All the zeros are=√5,-√5,3,-1

Answer 2

Answer:

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