MATH SOLVE

10 months ago

Q:
# What is the remainder when (3x3 – 2x2 + 4x – 3) is divided by (x2 + 3x + 3)?

Accepted Solution

A:

the complete question in the attached figure

we have that

(3x³ – 2x² + 4x – 3) is divided by (x² + 3x + 3)

(3x³ – 2x² + 4x – 3) is equals to------> 3x³+9x²+9x−11x²−33x−33+28x+30

=3x(x²+3x+3)−11(x²+3x+3)+28x+30

=(x²+3x+3)(3x−11)+28x+30

Hence[3x³−2x²+4x−3]/[x²+3x+3]=[(x²+3x+3)(3x−11)+28x+30]/[x²+3x+3]=[(3x−11)]+{[28x+30]/[x²+3x+3]}So the remainder of division is28x+30the answer is the option D) 28x+30

another way to make it more direct

(3x³ – 2x² + 4x – 3) is divided by║ (x² + 3x + 3)

-------------------------------------------- ║(3x-11)-3x³-9x²-9x---------------------------------------------11x²-5x-3----------------------------------------------+11x²+33x+33----------------------------------------------28x+30----------> this is the remainder

we have that

(3x³ – 2x² + 4x – 3) is divided by (x² + 3x + 3)

(3x³ – 2x² + 4x – 3) is equals to------> 3x³+9x²+9x−11x²−33x−33+28x+30

=3x(x²+3x+3)−11(x²+3x+3)+28x+30

=(x²+3x+3)(3x−11)+28x+30

Hence[3x³−2x²+4x−3]/[x²+3x+3]=[(x²+3x+3)(3x−11)+28x+30]/[x²+3x+3]=[(3x−11)]+{[28x+30]/[x²+3x+3]}So the remainder of division is28x+30the answer is the option D) 28x+30

another way to make it more direct

(3x³ – 2x² + 4x – 3) is divided by║ (x² + 3x + 3)

-------------------------------------------- ║(3x-11)-3x³-9x²-9x---------------------------------------------11x²-5x-3----------------------------------------------+11x²+33x+33----------------------------------------------28x+30----------> this is the remainder