Question

69. What is the remainder when (p^2 +2p^3-7p) is divided by (p^2 + 2)​

Answer 1

Rearrange the dividend (p²+2p³-7p) to (2p³+p²-7p).

Then use (p²+2) as divisor in the Division Algorithm of Polynomials .

Remainder is (-13p).

Refer the above picture for the details.

Answer 2

- (11p + 2) is the remainder.

Step-by-step explanation:

Given: Dividend = $p^2 +2p^3-7p$

Divisor = $p^2 + 2$

To Find: The remainder

Solution:

• Finding remainder by long division method

$p^2 + 2 \ \overline{) \ 2p^3 +p^2-7p \ ( } \ 2p+1\\{} \ \ \ \ \ \ \ \ \ \ \ 2p^3 \ \ \ \ \ \ \ + 4p\\{} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \overline{ \ p^2 - 11p}\\{} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ { \ p^2 + \ 2}\\{} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \overline{ \ - (11p+2)}$

Hence, - (11p + 2) is the remainder.