Step-by-step explanation:
We have to find (x³ - 5x² - 12x + 36)/(x - 6).
You can do this by the following methods:
- Long Division,
- Synthetic Division, or
- Comparing Coefficients
I have chosen to do by Comparing Coefficients.
x³ - 5x² - 12x + 36
= (x - 6)(Ax² + Bx + C)
= Ax³ + (B - 6A)x² + (C - 6B)x - 6C.
By Comparing Coefficients, we have:
- A = 1,
- B - 6A = -5,
- C - 6B = -12, and
- -6C = 36.
Solving them we have A = 1, B = 1, C = -6.
Therefore x³ - 5x² - 12x + 36
= (x - 6)(x² + x - 6)
= (x - 6)(x + 3)(x - 2).
Hence the other 2 dimensions are
(x + 3) and (x - 2).
