Asked by Danielle
                Divide using long division:   6x3 + 19x2 + x – 10 divided by 2x -1
Divide using synthetic division: 2x3 + 2x2 + 10 divided by x + 3
PLEASE HELP!
            
            
        Divide using synthetic division: 2x3 + 2x2 + 10 divided by x + 3
PLEASE HELP!
Answers
                    Answered by
            Damon
            
    ans.__________________
2x-1| 6x^3 +19 x^2 +x -10
ans. 3 x^2
________________________
2x-1| 6x^3 +19 x^2 +x -10
______6x^3 ______________
            
ans. 3 x^2
________________________
2x-1| 6x^3 +19 x^2 +x -10
______6x^3 - 3 x^2 ______________
_______0 +22 x^2 +x -10
ans. 3 x^2 +11 x
________________________
2x-1| 6x^3 +19 x^2 +x -10
______6x^3 - 3 x^2 ______________
_______ 0 +22 x^2 + x -10
___________+22 x^2 -11x____
___________________12x -10
ans. 3 x^2 +11 x +6
________________________
2x-1| 6x^3 +19 x^2 +x -10
______6x^3 - 3 x^2 ______________
_______ 0 +22 x^2 + x -10
___________+22 x^2 -11x____
___________________12x -10
___________________12 x-6
R = -4
=============================
_______2 2 0 10
-3_________________________
_______2
_______2 2 0 10
________-6
-3_________________________
_______2
_______2 2 0 10
________-6
-3_________________________
_______2 -4
_______2 2 0 10
________-6 12
-3_________________________
_______2 -4
_______2 2 0 10
________-6 12
-3_________________________
_______2 -4 12
_______2 2 0 10
________-6 12 -36
-3_________________________
_______2 -4 12
_______2 2 0 10
________-6 12 -36
-3_________________________
_______2 -4 12 -26
so
2x^2 -4x +12 remainder -26
    
2x-1| 6x^3 +19 x^2 +x -10
ans. 3 x^2
________________________
2x-1| 6x^3 +19 x^2 +x -10
______6x^3 ______________
ans. 3 x^2
________________________
2x-1| 6x^3 +19 x^2 +x -10
______6x^3 - 3 x^2 ______________
_______0 +22 x^2 +x -10
ans. 3 x^2 +11 x
________________________
2x-1| 6x^3 +19 x^2 +x -10
______6x^3 - 3 x^2 ______________
_______ 0 +22 x^2 + x -10
___________+22 x^2 -11x____
___________________12x -10
ans. 3 x^2 +11 x +6
________________________
2x-1| 6x^3 +19 x^2 +x -10
______6x^3 - 3 x^2 ______________
_______ 0 +22 x^2 + x -10
___________+22 x^2 -11x____
___________________12x -10
___________________12 x-6
R = -4
=============================
_______2 2 0 10
-3_________________________
_______2
_______2 2 0 10
________-6
-3_________________________
_______2
_______2 2 0 10
________-6
-3_________________________
_______2 -4
_______2 2 0 10
________-6 12
-3_________________________
_______2 -4
_______2 2 0 10
________-6 12
-3_________________________
_______2 -4 12
_______2 2 0 10
________-6 12 -36
-3_________________________
_______2 -4 12
_______2 2 0 10
________-6 12 -36
-3_________________________
_______2 -4 12 -26
so
2x^2 -4x +12 remainder -26
                    Answered by
            Danielle
            
    I'm a little confused by this. What is the answer to #1 or is 2x^2-4x+12 remainder -26 the answer? If so then how do I solve for #2? I'm sorry just some things come out funny when typed. 
    
                    Answered by
            Damon
            
    The answer to #1 is 3x^2+11x+6 remainder -4
Here is the last line of #1
ans. 3 x^2 +11 x +6
________________________
2x-1| 6x^3 +19 x^2 +x -10
______6x^3 - 3 x^2 ______________
_______ 0 +22 x^2 + x -10
___________+22 x^2 -11x____
___________________12x -10
___________________12 x-6
R = -4
then I put a line like this
==================================
and went on with the synthetic division.
In both cases I tried to only put one thing at a time, so copied over and over getting a little further into the problem each time
The answer to the synthetic division one is
2 x^2 - 4x + 12 reminder is -26
    
Here is the last line of #1
ans. 3 x^2 +11 x +6
________________________
2x-1| 6x^3 +19 x^2 +x -10
______6x^3 - 3 x^2 ______________
_______ 0 +22 x^2 + x -10
___________+22 x^2 -11x____
___________________12x -10
___________________12 x-6
R = -4
then I put a line like this
==================================
and went on with the synthetic division.
In both cases I tried to only put one thing at a time, so copied over and over getting a little further into the problem each time
The answer to the synthetic division one is
2 x^2 - 4x + 12 reminder is -26
                    Answered by
            Damon
            
    Here is the final version of the synthetic division one:
_______2 2 0 10
________-6 12 -36
-3_________________________
_______2 -4 12 -26
so
2x^2 -4x +12 remainder -26
like bring the 2 down
-3*that 2 = -6
2-6 goes below as -4
-3*-4 = +12 - that goes below the 0
0+12 = 12, bring it down
-3*12 = -36
add that to 10 to get remainder of -26
    
_______2 2 0 10
________-6 12 -36
-3_________________________
_______2 -4 12 -26
so
2x^2 -4x +12 remainder -26
like bring the 2 down
-3*that 2 = -6
2-6 goes below as -4
-3*-4 = +12 - that goes below the 0
0+12 = 12, bring it down
-3*12 = -36
add that to 10 to get remainder of -26
                    Answered by
            Damon
            
    2x3 + 2x2 + 10
By the way, important to write that as
2x^3 +2x^2 + 0x + 10
If you leave the zero coefficient terms of the polynomial out, you get messed up worse with columns and such. That is exactly why they had no coefficient of x, to make you figure that out.
    
By the way, important to write that as
2x^3 +2x^2 + 0x + 10
If you leave the zero coefficient terms of the polynomial out, you get messed up worse with columns and such. That is exactly why they had no coefficient of x, to make you figure that out.
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