Question

divide and verify the division algorithm of p(x)=3x^3+x^2+2x+5 by 1+2x+x^2​

Answer 1

Answer:

$3x - 5 + \frac{9x + 10}{ {x}^{2} + 2x + 1 }$

Step-by-step explanation:

Please refer the attached image for division steps

To verify

$Dividend =Divisor*Quotient + Remainder \\ Dividend =( {x}^{2} + 2x + 1)(3x - 5) + 9x + 10 \\ Dividend =3 {x}^{3} + 6 {x}^{2} + 3x - 5 {x}^{2} - 10x - 5 + 9x + 10 \\ Dividend =3 {x}^{3} + {x}^{2} + 2x + 5$

Which is equal to the dividend