Question

divide polynomials and verify division algorithm
divide (2x^5-5x^4+7x^3+4x^2-x+11) by (x^3+2)​

Answer 1

Answer:

(2x5-5x4+7x3+4x2-10x+11)/(x3+2)  

Final result :

2x5 - 5x4 + 7x3 + 4x2 - 10x + 11 ———————————————————————————————— x3 + 2

See results of polynomial long division:

1. In step #05.05

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "x3"   was replaced by   "x^3".  4 more similar replacement(s).

Step by step solution :

Step  1  :

Equation at the end of step  1  :

Step  2  :

Equation at the end of step  2  :

Step  3  :

Equation at the end of step  3  :

Step  4  :

Equation at the end of step  4  :

Step  5  :

2x5 - 5x4 + 7x3 + 4x2 - 10x + 11 Simplify ———————————————————————————————— x3 + 2

Trying to factor by pulling out :

5.1      Factoring:  2x5 - 5x4 + 7x3 + 4x2 - 10x + 11  

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1:  4x2 + 7x3  

Group 2:  2x5 - 5x4  

Group 3:  -10x + 11  

Pull out from each group separately :

Group 1:   (7x + 4) • (x2)

Group 2:   (2x - 5) • (x4)

Group 3:   (-10x + 11) • (1) = (10x - 11) • (-1)

Looking for common sub-expressions :

Group 1:   (7x + 4) • (x2)

Group 3:   (10x - 11) • (-1)

Group 2:   (2x - 5) • (x4)

Step-by-step explanation: