if the polynomial p(x) is devided by x^2 + 4x + 2, then the quotient polynomial x^@ - 4x + 14 and the remainder polynomial 9x-13 are obtained. find polynomial p(x)

Answer : Given : if the polynomial p(x) is devided by x^2 + 4x + 2, then the quotient polynomial x^@ - 4x + 14 and the remainder polynomial 9x-13 are obtained

To find p(x)

 

Dividend = p(x)

divisor :  x² + 4x + 2

quotient: x² - 4x + 14

remainder 9x-13 

 

we know , 

Dividend = divisor * quotient + remainder  

=> p(x) = ( ( x² + 4x + 2 ) * ( x² - 4x + 14 ) ) + ( 9x-13)

=> p(x) = ( x⁴ + 48x + 28 ) + ( 9x-13)

=> p(x) = (x⁴ + 57x + 15 ) Answer