![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). class=](https://us-static.z-dn.net/files/db0/085b8adad14cb024a560dc762c1bc767.png)
The result in form of q(x) + r(x)/b(x) is [tex]=3 x^{2}+x-1+\frac{7}{(x+1)}[/tex]
Solution:
Need to divide [tex]3 x^{3}+4 x^{2}+6 \text { by } x+1[/tex]
The image for the division is attached below
Step 1: here x + 1 is dividend and [tex]3 x^{3}+4 x^{2}+6[/tex] 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) [tex]=3 x^{2}+x-1[/tex] remainder r = 7 and dividend b(x) = x+1
Expressing it in [tex]q(x)+\frac{r(x)}{b(x)}[/tex] we get,
[tex]=3 x^{2}+x-1+\frac{7}{(x+1)}[/tex]
