I am supposed to preform the indicated divisons:
8x^3-6x^2+2x divided by 4x+1
would the answer be 2x^2+1x 1x/4x+1??
its 2x^2 - 2x + 1 with a remainder of -1
To perform the division of the given expression, 8x^3 - 6x^2 + 2x, divided by 4x + 1, you can use polynomial long division. Here's how you can do it:
Step 1: Write the division problem in the proper format, with the divisor on the left and the dividend on the right:
_____________________
4x + 1 | 8x^3 - 6x^2 + 2x
Step 2: Divide the first term of the dividend (8x^3) by the first term of the divisor (4x). The result is 2x^2.
2x^2
_____________________
4x + 1 | 8x^3 - 6x^2 + 2x
Step 3: Multiply the entire divisor (4x + 1) by the quotient from Step 2 (2x^2). Write the result under the dividend:
2x^2
_____________________
4x + 1 | 8x^3 - 6x^2 + 2x
-(8x^3 + 2x^2)
Step 4: Subtract the product obtained in Step 3 from the dividend. Bring down the next term from the dividend (-6x^2):
2x^2
_____________________
4x + 1 | 8x^3 - 6x^2 + 2x
-(8x^3 + 2x^2)
_____________
-8x^2 + 2x
Step 5: Repeat the process until you have subtracted all the terms of the divisor from the dividend. Bring down the next term from the dividend (2x):
2x^2 + (2x/4x) = 2x^2 + 1/2
_____________________
4x + 1 | 8x^3 - 6x^2 + 2x
-(8x^3 + 2x^2)
_____________
-8x^2 + 2x + (2x/4x) = -8x^2 + 2x + 1/4
Step 6: Repeat the process until you have subtracted all the terms of the divisor from the dividend. In this case, there are no more terms in the dividend. The final result is the quotient you obtained during the process:
2x^2 + 1/2 + (1/4x)
_____________________
4x + 1 | 8x^3 - 6x^2 + 2x
Therefore, the correct division of the expression 8x^3 - 6x^2 + 2x, divided by 4x + 1, is: 2x^2 + 1/2 + (1/4x).
Note: It's important to double-check the calculations to ensure accuracy.