What is the remainder when (3x^3-2x^2+4x-3) is divided by (x^2+3x+3)?

The remainder is 28x+30

Step-by-step explanation:

We will divide  3x^3-2x^2+4x-3 by x^2+3x+3.

To get the first term of the dividend we will multiply x^2+3x+3 by 3x

 3x(x^2+3x+3)

=3x^3+9x^2+9x

It means    

     x^2+3x+3) 3x^3-2x^2+4x-3(  3x -11  

                       3x^3+9x^2+9x

                   -           -         -

                                   11x^2-5x-3       (Now multiply x^2+3x+3 by -11 to get the

                                   11x^2-33x-33     first term)

                              -            +      +

                                          28x+30

We can not solve it further because remainder has two terms and divisor has 3 terms. Therefore the remainder is 28x+30

step-by-step explanation:

the ratio of red paint to blue paint is always 9/7. that means that, whatever x's value, (4x+12)/(4x-4) has that same ratio. so, set up an equation and cross-multiply to solve for x:

9/7 = (4x+12)/(4x-4)

9(4x-4) = 7(4x+12)

36x - 36 = 28x + 84

8x - 36 = 84

8x = 120

x = 15

answer: 8

step-by-step explanation: if you add the possibilities 5 different flavor and 3 different sizes 5+3=8