Question

Divide 6x3+13x2+x-2 by 2x+1 and find the quotient and remainder and also verify division algorithm

Answer 1

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Answer 2

Answer:

$Quotient=q=3x^2+5x-2$

$Remainder=r=0$

Step-by-step explanation:

Given the polynomial

$P(x)=6x^3+13x^2+x-2$

we have to find the quotient and remainder when above polynomial is divided by 2x+1

The division is shown in attachment

The quotient and remainder is

$Quotient=q=3x^2+5x-2$

$Remainder=r=0$

By division algorithm

$Dividend=Divisor\times Quotient + Remainder$

$P(x)=(2x+1)\times (3x^2+5x-2)+0$

$P(x)=2x(3x^2+5x-2)+1(3x^2+5x-2)$

$P(x)=6x^3+10x^2-4x+(3x^2+5x-2)$

$P(x)=6x^3+13x^2+x-2$

which is verified