Question

What is the result when 3x3 + 4x2 + 6 is divided by x + 1? If there is a remainder,

express the result in the form q(x) + ][2).

Answer 1

The result in form of q(x) + r(x)/b(x) is
`=3 x^(2)+x-1+(7)/((x+1))`

Solution:

Need to divide
`3 x^(3)+4 x^(2)+6 \text { by } x+1`

The image for the division is attached below

Step 1: here x + 1 is dividend and
`3 x^(3)+4 x^(2)+6` is divisor

Step 2: Divide the first term of numerator by first term of denominator and place it in quotient

Step 3: Multiply the denominator by that answer and put that below the numerator

Step 4: Subtract to obtain a new polynomial

Step 5: Repeat using the new polynomial until no variable “x’ is left in remainder

On dividing we get quotient q(x)
`=3 x^(2)+x-1` remainder r = 7 and dividend b(x) = x+1

Expressing it in
`q(x)+(r(x))/(b(x))` we get,

`=3 x^(2)+x-1+(7)/((x+1))`