find the value of k if P of X equal to 3 x cube minus 3 X square + a x + 15 leaves remainder -9 when divided by x minus 3
Answers
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,
By division theorem,Dividend=divisor×quotient+ remainder
By division theorem,Dividend=divisor×quotient+ remainderDividend=F(x)
By division theorem,Dividend=divisor×quotient+ remainderDividend=F(x)Divisor=x^2–5
By division theorem,Dividend=divisor×quotient+ remainderDividend=F(x)Divisor=x^2–5Quotient=x^2–2x-3
By division theorem,Dividend=divisor×quotient+ remainderDividend=F(x)Divisor=x^2–5Quotient=x^2–2x-3Remainder=0,then
By division theorem,Dividend=divisor×quotient+ remainderDividend=F(x)Divisor=x^2–5Quotient=x^2–2x-3Remainder=0,thenF(x)=(x^2–5)(x^2–2x-3)
By division theorem,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
By division theorem,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)
By division theorem,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