Use Long Division

Question

When you use long division to divide 15x⁵ - 2x⁴ + 12x³ - 4x² + x - 3  by 3x^3 + 2x^2+ 7x- 2 , the standard form of the result is _[blank 1]_ + _[blank 2]_ + _[blank 3]_, with a remainder of 44x² + 28x - 13 . What is the answer for all three?

Answer 1

The three blanks are 5x² - 4x - 5.

I will do my best to show the work below, I hope the formatting doesn't mess anything up.

| 5x² - 4x - 5

3x³ + 2x² + 7x - 2 | 15x⁵  - 2x⁴  + 12x³ - 4x² + x - 3

-(15x⁵ + 10x⁴ + 35x³ -10x²)

-12x⁴ - 23x³ + 6x² + x - 3

-(-12x⁴ - 8x³ - 28x² + 8x)

-15x³ + 34x² - 7x - 3

-(15x³ - 10x² -35x + 10)

44x² + 28x -13 <---- Remainder