Question

when a polynomial p(x) is divided by 3x-1, the quotient and remainder are x²+3x-2 and 4 respectively. Find p(x)​

Answer 1

Given question -:

when a polynomial p(x) is divided by 3x-1, the quotient and remainder are x²+3x-2 and 4 respectively. Find p(x)

let's try to solve the question

According to Division Algorithm

dividend = divisor × quotient + remainder

Now

$dividend \: = 3x + 1( {x}^{2} + 3x - 2) + 4$

$3 {x}^{3} + 9 {x}^{2} - 6x - {x}^{2} - 3x - 2 + 4$

$3 {x}^{3}+ 8 {x}^{2} - 9x + 2$

Hence dividend =

$3 {x}^{3} + {x}^{2} - 9x + 2$

Hope this will help you

Thank you ..