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!

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

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.

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 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

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.

Sure! I can help you with both long division and synthetic division.

To divide using long division, follow these steps:

Step 1: Write down the dividend (the expression being divided) and the divisor (the expression you are dividing by), making sure to organize them in descending order of degree.

Dividend: 6x^3 + 19x^2 + x - 10
Divisor: 2x - 1

Step 2: Divide the leading term of the dividend (in this case, 6x^3) by the leading term of the divisor (2x), and write the result as the first term of the quotient.

Quotient: 3x^2

Step 3: Multiply the divisor by the first term of the quotient and subtract the result from the dividend. Write the resulting expression below the dividend.

3x^2
________________________
2x - 1 | 6x^3 + 19x^2 + x - 10
- (6x^3 - 3x^2)
________________________
22x^2 + x - 10

Step 4: Bring down the next term from the dividend (in this case, + x) and repeat steps 2 and 3 until you have subtracted all terms from the dividend.

Quotient: 3x^2 + 11x + 5

Hence, the long division result is: 3x^2 + 11x + 5.

Now, let's move on to synthetic division.

To divide using synthetic division, follow these steps:

Step 1: Write down the dividend (the expression being divided) and the divisor (the expression you are dividing by) in their simplified forms, making sure to organize them in descending order of degree.

Dividend: 2x^3 + 2x^2 + 10
Divisor: x + 3

Step 2: Change the sign of the divisor and write down its constant term (-3) in the leftmost column.

-3

Step 3: Write down the coefficients of the dividend in a row, in descending order of degree.

2 2 10

Step 4: Bring down the first term of the dividend (in this case, 2) and write it below the line.

-3
2

Step 5: Multiply the number at the bottom of the column by the divisor's constant term (-3), and write the result below the next coefficient of the dividend.

-3
2
-6

Step 6: Add the two numbers in the new column and write the sum below the line.

-3
2
-6
-4

Step 7: Repeat steps 5 and 6 until you have gone through all the coefficients of the dividend.

-3
2
-6
-4
6

Step 8: The number in the bottom row (6 in this case) is the remainder. The remaining numbers in the row, from left to right, form the quotient.

Quotient: 2x^2 - 4
Remainder: 6

Hence, the synthetic division result is: 2x^2 - 4 with a remainder of 6.

I hope this helps! Let me know if you have any further questions.