Step-by-step explanation:
Easiest way is to use synthetic division, but I am going to use comparing coefficients because I have my phone:
x³ + 6x² - 5x
= (x - 2)(Ax² + Bx + C) + D
= Ax³ + (B - 2A)x² + (C - 2B)x + (D - 2C)
By Comparing Coefficients, we have
A = 1
B - 2A = 6
C - 2B = -5
D - 2C = 0
Solving, we have A = 1, B = 8, C = 11, D = 22.
Hence x³ + 6x² - 5x
= (x - 2)(x² + 8x + 11) + 22.
