On dividing 3x3+x2+2x+5 by a polynomial g(x), the quotient and remainder are (3x-5) and (9x+10) respectively. Find g(x).
Given quotient = (3x-5)
remainder = (9x+10)
divident = 3x3+x2+2x+5
By division algorithm divident=divisor×quotiant+reminder
3x3+x2+2x+5=g(x)×(3x−5)+(9x+10)
3x3+x2+2x+5−(9x+10)=g(x)×(3x−5)
3x3+x2−7x−5=g(x)×(3x−5)
g(x)=3x3+x2−7x−53x−5
g(x)=