solve: 2x^2-3x+5 divided by 2x-1
go to calc101.com and click on the long division link. It will show all the steps involved.
To divide the polynomial 2x^2 - 3x + 5 by 2x - 1, we can use long division. Here are the steps:
Step 1: Divide the first term of the dividend by the first term of the divisor: 2x^2 ÷ 2x = x.
Step 2: Multiply the divisor by the quotient from the previous step: (2x - 1) * x = 2x^2 - x.
Step 3: Subtract the result from the original dividend: (2x^2 - 3x + 5) - (2x^2 - x) = -2x + 5.
Step 4: Bring down the next term from the original dividend, which is -2x: -2x + 5.
Step 5: Repeat steps 1 to 3 using the new dividend (-2x + 5).
Step 6: Divide the first term of the new dividend by the first term of the divisor: -2x ÷ 2x = -1.
Step 7: Multiply the divisor by the quotient from the previous step: (2x - 1) * -1 = -2x + 1.
Step 8: Subtract the result from the new dividend: (-2x + 5) - (-2x + 1) = 4.
Step 9: Since there are no more terms in the dividend, we have reached the remainder, which is 4.
Therefore, the result of the division is x - 1 with a remainder of 4.
To divide the polynomial 2x^2 - 3x + 5 by 2x - 1, you can use long division. Follow these steps:
Step 1: Write the polynomial in descending order.
2x^2 - 3x + 5 divided by 2x - 1
Step 2: Divide the first term of the dividend (2x^2) by the first term of the divisor (2x). The result is x.
x
---
2x - 1 | 2x^2 - 3x + 5
Step 3: Multiply the divisor (2x - 1) by the quotient (x), and write the result below the line.
x
---
2x - 1 | 2x^2 - 3x + 5
- (2x^2 - x)
Step 4: Subtract the result from the dividend.
x
---
2x - 1 | 2x^2 - 3x + 5
- (2x^2 - x)
----------
-2x + 5
Step 5: Bring down the next term from the dividend (-2x).
x - 2
Step 6: Divide the term (-2x) by the first term of the divisor (2x). The result is -1.
x - 2
---
2x - 1 | 2x^2 - 3x + 5
- (2x^2 - x)
----------
-2x + 5
+ (2x - 1)
Step 7: Multiply the divisor (2x - 1) by the quotient (-1), and write the result below the line.
x - 2
---
2x - 1 | 2x^2 - 3x + 5
- (2x^2 - x)
----------
-2x + 5
+ ( 2x - 1)
-----------
+4
Step 8: Subtract the result from the dividend.
x - 2 + (4 / (2x - 1))
Step 9: Since there are no more terms to bring down, the division is complete.
x - 2 + 4 / (2x - 1)
Therefore, the result of dividing 2x^2 - 3x + 5 by 2x - 1 is x - 2 + 4 / (2x - 1).