SOLUTION: divide the polynomials using long division. Then verify your solution by using synthetic division. Show your work. (-2x^3 + 5x^2

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Question 1206090: divide the polynomials using long division. Then verify your solution by using synthetic division. Show your work.
(-2x^3 + 5x^2 - x + 2) ÷ (x + 2)

Found 3 solutions by josgarithmetic, MathLover1, math_tutor2020:
Answer by josgarithmetic(39618)   (Show Source):
You can put this solution on YOUR website!
duplicate

Should be result as .

Answer by MathLover1(20850)   (Show Source):
You can put this solution on YOUR website!

using long division
...........(
|
........................subtract
.................................bring down
......................
.................................subtract
.........................................bring down
...............................
.........................................subtract
....................................... => reminder

verify solution by using synthetic division
Write the coefficients of the dividend to the right.
.....||||
|...|...|...|...|

Write down the first coefficient without changes:

We have obtained the following resulting coefficients:
,,, (the last coefficient is the remainder)
the quotient is , and the remainder is

Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!

Answers:
quotient = -2x^2+9x-19
remainder = 40

Here's the polynomial long division

The expression at the very top is the quotient. The number at the very bottom is the remainder.

And here's what the synthetic division looks like

The last number in the bottom row is the remainder.
The other values in the bottom row are the coefficients to the quotient.

Side note: The nonzero remainder indicates that (x+2) is NOT a factor of -2x^3 + 5x^2 - x + 2

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There are many great resources found on the internet that will explain how polynomial long division works.
Here is one such page
https://www.mathsisfun.com/algebra/polynomials-division-long.html
Feel free to explore other resources.

Here is a calculator that will provide a step by step look for your particular problem
https://www.emathhelp.net/en/calculators/algebra-1/polynomial-long-division-calculator/

Here is a calculator for synthetic division
https://www.emathhelp.net/en/calculators/algebra-1/synthetic-division-calculator/
This calculator also explains things step by step.

SOLUTION: divide the polynomials using long division. Then verify your solution by using synthetic division. Show your work. (-2x^3 + 5x^2 - x + 2) ÷ (x + 2)