Questions: Divide using polynomial long division. (2 x^2-3 x+1) ÷ (x+5)

Divide using polynomial long division. (2 x^2-3 x+1) ÷ (x+5)
Transcript text: Divide using polynomial long division. \[ \left(2 x^{2}-3 x+1\right) \div(x+5) \]
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Solution

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Solution Steps

Step 1: Polynomial Long Division

To divide the polynomial \( 2x^2 - 3x + 1 \) by \( x + 5 \), we perform polynomial long division. The process yields a quotient and a remainder.

Step 2: Results of the Division

The results of the division are:

  • Quotient: \( 2x - 13 \)
  • Remainder: \( 66 \)
Step 3: Complete Division Expression

The complete expression for the division can be written as: \[ 2x - 13 + \frac{66}{x + 5} \]

Final Answer

The final result of the division \( \left(2x^2 - 3x + 1\right) \div (x + 5) \) is: \[ \boxed{2x - 13 + \frac{66}{x + 5}} \]

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