Question

​ Find the remainder when f(x) = x3 – 6x2 + 9x + 7 is divided by g(x) = x – 1

Answer 1

(x) = x3 – 6x2 + 9x + 7 is divided by g(x) = x – 1 Put x=1 F (1)=1×1×1-6×1×1+9×1+7 =1-6+9+7 =11

Answer 2

Dividing :  x3 - 6x2 + 9x + 7 
                              ("Dividend")
By         :    x - 1    ("Divisor")

dividend  x3 - 6x2 + 9x + 7 - divisor * x2   x3 - x2     remainder  - 5x2 + 9x + 7 - divisor * -5x1   - 5x2 + 5x   remainder      4x + 7 - divisor * 4x0       4x - 4 remainder        11 

Quotient :  x2 - 5x + 4  
Remainder :  11  

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