High School

What is the remainder when [tex]$3x^3 – 2x^2 + 4x – 3$[/tex] is divided by [tex]$x^2 + 3x + 3$[/tex]?

A) 30
B) 3x – 11
C) 28x – 36
D) 28x + 30

Answer :

Answer:

D) 28x+30

Step-by-step explanation:

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The correct option is: D) 28x+30

Explanation

We will divide [tex](3x^3 - 2x^2 + 4x - 3)[/tex] by [tex](x^2 + 3x + 3)[/tex] using long division method.

3x- 11

[tex]x^2+3x+3) \overline{3x^3-2x^2+4x-3}[/tex]

-(3x³+9x²+9x)

-11x²- 5x - 3

-(-11x²- 33x - 33)

28x +30


So, the remainder will be: [tex]28x+30[/tex]

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