If we divide the polynomial x4 4x3 2x2 x 4 by x2 3x, what will be the remainder

To solve, first rewrite the equation:

(x^4 + 4x^3 +2x^2 + x + 4) / (x^2 + 3x)

1. Then, you will divide the term with the highest power in the numerator (x^4) by the term in the denominator with the highest power (x^2). When exponents are involved in dividing, you simply subtract them from one another:

x^4 / x^2 = x^2

2. Now, you will multiply this answer by the denominator:

x^2 (x^2 + 3x) = x^4 + 3x^3

3. Next, subtract this answer from the numerator, and bring down the rest:

(x^4 + 4x^3 + 2x^2 + x + 4)
-x^4 - 3x^3
         = x^3 + 2x^2 + x + 4 

Now, repeat the steps until you're at the simplest form:

1. x^3 / x^2 = x

2. x (x^2 + 3x) = x^3 + 3x^2

3. x^3 + 2x^2 + x + 4
   -x^3 - 3x^2
           = -x^2 + x + 4

1. -x^2 / x^2 = -1

2. (-1) (x^2 + 3x) = -x^2 - 3x

3. -x^2 + x + 4
    +x^2 + 3x
           = 4x + 4