SOLUTION: What should be added to 6x^3+13x^2+4x+20, so that it becomes exactly divisible by 2+x^2? Solve through synthetic division -8x+6 -8x-6 8x-6 8x+6

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> SOLUTION: What should be added to 6x^3+13x^2+4x+20, so that it becomes exactly divisible by 2+x^2? Solve through synthetic division -8x+6 -8x-6 8x-6 8x+6      Log On


   

Question 1133536: What should be added to 6x^3+13x^2+4x+20, so that it becomes exactly divisible by 2+x^2? Solve through synthetic division
-8x+6
-8x-6
8x-6
8x+6
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
............(6x%2B13
x%5E2%2B2|6x%5E3%2B13x%5E2%2B4x%2B20

..............6x%5E3%2B12x .....subtract
...................13x%5E2-8x%2B20+
...................13x%5E2%2B0%2Ax%2B26+
.........................-8x-6+ => reminder

6x%5E3%2B13x%5E2%2B4x%2B20=6+x+%2B+13%2B%28-8x-6%29%2F%28x%5E2%2B2%29

answer: for 6x%5E3%2B13x%5E2%2B4x%2B20 to become exactly divisible by 2%2Bx%5E2 we should to add reminder:


now, move -%288x%2B6%29%2F%28x%5E2%2B2%29 to the left

6x%5E3%2B13x%5E2%2B4x%2B20%2B8x%2B6=%286x%2B13%29%28x%5E2%2B2%29
so, we added 8x%2B6+, and we have

+6+x%5E3+%2B+13+x%5E2+%2B+12+x+%2B+26+=+%286+x+%2B+13%29+%2A+%28x%5E2+%2B+2%29+%2B+0