Question

Divide the first polynomial by the second polynomial in each of the following. Also write the quotient and remainder. 6. 6x^2-31x+47 by 2x-5​

Answer 1

Step-by-step explanation:

Let, p(x)=6x

2

−31x+47,

g(x)=2x−5

q(x)=3x−8

and r=7

∴ By division algorithm,

p(x)=g(x)×q(x)+r

=(2x−5)(3x−8)+7

=6x

2

−15x−16x+40+7

=6x

2

−31x+47

=p(x)

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Answer 2

Answer:

Let, p(x)=6x2−31x+47,

g(x)=2x−5

q(x)=3x−8 

and r=7

∴ By division algorithm, 

p(x)=g(x)×q(x)+r

         =(2x−5)(3x−8)+7

         =6x2−15x−16x+40+7

         =6x2−31x+47

        =p(x)

Hence division algorithm is verified.