Question

divide2x^3+3x^2+4x+10 by x^2+x+1 and verify that dividend = Quotient×divisor+Reminder
plz give me the full explanation ​

Answer 1

Answer :

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Step-by-step explanation:

We know that the division algorithm states that:

We know that the division algorithm states that: Dividend=(Divisor×quotient)+Remainder

We know that the division algorithm states that: Dividend=(Divisor×quotient)+RemainderHere it is given that the dividend is p(x)=4x

We know that the division algorithm states that: Dividend=(Divisor×quotient)+RemainderHere it is given that the dividend is p(x)=4x 3+2x 2 −10x+2, the divisor is g(x), the quotient is 2x 2 +4x+1 and the remainder is 5,

therefore,

therefore,4x 3 +2x 2 −10x+2=[g(x)(2x 2 +4x+1)]+5⇒g(x)=2x 2+4x+14x 3 +2x 2 −10x+2

therefore,4x 3 +2x 2 −10x+2=[g(x)(2x 2 +4x+1)]+5⇒g(x)=2x 2+4x+14x 3 +2x 2 −10x+2

therefore,4x 3 +2x 2 −10x+2=[g(x)(2x 2 +4x+1)]+5⇒g(x)=2x 2+4x+14x 3 +2x 2 −10x+2 The division is shown above.

therefore,4x 3 +2x 2 −10x+2=[g(x)(2x 2 +4x+1)]+5⇒g(x)=2x 2+4x+14x 3 +2x 2 −10x+2 The division is shown above.Hence, from the above division, we get that the divisor is g(x)=2x−3