Question

on dividing 3x3+x2+2x+5 by a polynomial gx the quotient and remainder are 3x-5and 9x+10 respectively find gx.

Answer 1

heya _______________


$ans = \: x {}^{2} + 2x + 1$
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Answer 2

Given :

Given polynomial or dividend is :

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

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 :

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

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

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

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

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

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