Question

What is the remainder when (3x3 â€"" 2x2 4x â€"" 3) is divided by (x2 3x 3)?.

Answer 1

The remainder of the equation is $\rm 28x+30$.

Given that,

When the equation $\rm 3x^3-2x^2+4x-3$ is divided by $\rm x^2+3x+3$.

We have to find,

The remainder of the equation?

According to the question,

The equation $\rm 3x^3-2x^2+4x-3$ is divided by $\rm x^2+3x+3$.

On the division of the polynomial, the remainder is,

$\dfrac{\rm 3x^3-2x^2+4x-3}{\rm x^2+3x+3}$

Factorize the equation to convert this into the simplest form,

$\rm 3x^3-2x^2+4x-3\\\\3x^3-11x^2+9x^2+9x+28x-33x-33+30\\\\Taking \ the \ common \ terms \ and \ simplify\ the\ equation\\\\3x^3+9x^2+9x+11x^2+33x-33+28x+30\\\\3x(x^2+3x+3) - 11(x^2+3x+3) + 28x+30\\\\(3x+11) (x^2+3x+3) +28x +30$

Now, the equation can be written as,

$\rm = \dfrac{(3x+11) (x^2+3x+3) +28x +30}{ x^2+3x+3}\\\\= \dfrac{(3x+11) (x^2+3x+3) }{ x^2+3x+3} + \dfrac{28x +30}{ x^2+3x+3}\\\\= (3x+11) + \dfrac{28x +30}{ x^2+3x+3}$

The relation between the divisor, remainder, and quotient is,

$\rm = Quotient + \dfrac{Remainder}{Divisor}$

On comparing with the equation,

The remainder becomes 28x +30.

Hence, The required remainder of the equation is $\rm 28x+30$.

For more details refer to the link given below.

brainly.com/question/25880057