How do you divide #(2x^3+9x^2-9x+1) / (2x-3) # using polynomial long division?

Answer 1

#(2x^3+9x^2-9x+1)/(2x-3)=x^2+6x+9/2+(29/2)/(2x-3)#

We divide by long division method #" " " " " " " underline(x^2+6x+9/2)# #2x-3|~2x^3+9x^2-9x+1# #" " " " " "underline(2x^3-3x^2" " " " " " " ")# #" " " " " " " " " "12x^2-9x+1# #" " " " " " " " " "underline(12x^2-18x" " " )# #" " " " " " " " " " " " " " "+9x+1# #" " " " " " " " " " " " " "underline(+9x-27/2" " " )# #" " " " " " " " " " " " " " " " " " "+29/2#

The outcome is

#(2x^3+9x^2-9x+1)/(2x-3)=x^2+6x+9/2+(29/2)/(2x-3)#

Checking:

#"Divisor x Quotient"+"Remainder"="Dividend"#
#(2x-3)(x^2+6x+9/2)+29/2=2x^3+12x^2+9x-3x^2-18x-27/2+29/2#
#(2x-3)(x^2+6x+9/2)+29/2=2x^3+9x^2-9x-27/2+29/2#
#(2x-3)(x^2+6x+9/2)+29/2=2x^3+9x^2-9x+2/2#
#(2x-3)(x^2+6x+9/2)+29/2=2x^3+9x^2-9x+1#

May God bless you all. I hope this explanation helps.

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Answer 2

To divide (2x^3+9x^2-9x+1) by (2x-3) using polynomial long division, follow these steps:

  1. Arrange the dividend (2x^3+9x^2-9x+1) and the divisor (2x-3) in descending order of exponents.
  2. Divide the first term of the dividend (2x^3) by the first term of the divisor (2x). The result is x^2.
  3. Multiply the divisor (2x-3) by the quotient obtained in step 2 (x^2). The result is 2x^3-3x^2.
  4. Subtract the product obtained in step 3 from the dividend. (2x^3+9x^2-9x+1) - (2x^3-3x^2) = 12x^2-9x+1.
  5. Bring down the next term from the dividend (-9x).
  6. Divide the first term of the new dividend (12x^2) by the first term of the divisor (2x). The result is 6x.
  7. Multiply the divisor (2x-3) by the quotient obtained in step 6 (6x). The result is 12x^2-18x.
  8. Subtract the product obtained in step 7 from the new dividend. (12x^2-9x+1) - (12x^2-18x) = 9x+1.
  9. Bring down the next term from the dividend (9x).
  10. Divide the first term of the new dividend (9x) by the first term of the divisor (2x). The result is 4.5.
  11. Multiply the divisor (2x-3) by the quotient obtained in step 10 (4.5). The result is 9x-13.5.
  12. Subtract the product obtained in step 11 from the new dividend. (9x+1) - (9x-13.5) = 14.5.
  13. There are no more terms to bring down, and the remainder (14.5) is less than the divisor (2x-3).
  14. The final quotient is x^2 + 6x + 4.5, and the remainder is 14.5.
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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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