Question

on dividing 3x^3+x^2+2x+5 by a polynomial g(x), the quotient and remainder are (3x-5) and (9x+10) respectively. find (g).​

Answer 1

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Step-by-step explanation:

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Answer 2

Answer:

Given polynomial or dividend is :

= 3x^{3} + x^{2} +2x + 5=3x

3

+x

2

+2x+5

The quotient so obtained :

= 3x - 5

And the remainder ;

= 9x + 10

To Find :

The divisor or polynomial g(x) = ?

Solution :

Since we know that by Euclid division lemma , we have :

Dividend = divisor \times× quotient + remainder

So on applying this and putting the given values here we can find g (x) as :

3x^{3} + x^{2} +2x + 5 = g (x) \times (3x-5) +(9x+10)3x

3

+x

2

+2x+5=g(x)×(3x−5)+(9x+10)

Or ,( 3x^{3} + x^{2} +2x + 5) - (9x+10) = g(x) \times (3x-5)(3x

3

+x

2

+2x+5)−(9x+10)=g(x)×(3x−5)

Or,g(x) = \frac{ 3x^{3} + x^{2} -7x - 5}{3x - 5}g(x)=

3x−5

3x

3

+x

2

−7x−5

So after solving the above equation we can easily get g(x) as :

g(x) = x^{2} + 2x + 1g(x)=x

2

+2x+1

So finally the value of polynomial g (x) is x^{2} + 2x + 1x

2

+2x+1 .