Divide the polynomials. x^3+6x^2-5x by x-2

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.

32

step-by-step explanation: