Question

Using the long division method, find quotient and remainder of the following polynomial. p(x) = x + 3x² + 3x + 1 and g(x)=x+2​

Answer 1

Answer:

Divide (x +2) into (x^3 +3x^2 +3x +1):

Before you start make sure the powers are in descending order.

Dividing equations is just like division with numbers.

Look at the first set of values: x^3 .

You need to remove them form the equation by multiplying (x + 2) by x^2,

this gives you x^3 + 2 x^2. Take this value and subtract it from the equation.

You now have x^2 + 3 x + 1 left in the equation.

Look at the next set of values: x^2.

You need to remove them form the equation by multiplying (x + 2) by x,

this gives you x^2 + 2 x. Take this value and subtract it from the equation.

You now have x + 1 left in the equation.

By multiplying x + 2 by 1 and subtract form x + 1.

You have a remainder of -1 or (-1/(x +2))

The answer to this problem is: x^2 +x + 1 + ((-1)/(x +2))