(x2+x−17)÷(x−4)=

Jasonbradley

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Jun 17, 2024

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Solving the Polynomial Division: (x² + x - 17) ÷ (x - 4)

This article will guide you through the process of dividing the polynomial (x² + x - 17) by (x - 4). We will use the method of long division to solve this problem.

Long Division Steps

1. Set up the division: Write the dividend (x² + x - 17) inside the division symbol and the divisor (x - 4) outside.

        _______
   x - 4 | x² + x - 17
   

2. Divide the leading terms: Divide the leading term of the dividend (x²) by the leading term of the divisor (x). This gives us x. Write this quotient above the x² term in the dividend.

        x      
   x - 4 | x² + x - 17
   

3. Multiply the quotient by the divisor: Multiply the quotient (x) by the entire divisor (x - 4) and write the result below the dividend.

        x      
   x - 4 | x² + x - 17
           x² - 4x 
   

4. Subtract: Subtract the result from the dividend. Be sure to distribute the negative sign.

        x      
   x - 4 | x² + x - 17
           x² - 4x 
           -------
                 5x - 17
   

5. Bring down the next term: Bring down the next term (-17) from the dividend.

        x      
   x - 4 | x² + x - 17
           x² - 4x 
           -------
                 5x - 17 
   

6. Repeat steps 2-5: Repeat the process by dividing the leading term of the new dividend (5x) by the leading term of the divisor (x). This gives us 5. Write this quotient above the -17.

        x + 5     
   x - 4 | x² + x - 17
           x² - 4x 
           -------
                 5x - 17 
                 5x - 20 
   

7. Subtract: Subtract the result from the new dividend.

        x + 5     
   x - 4 | x² + x - 17
           x² - 4x 
           -------
                 5x - 17 
                 5x - 20 
                 -------
                       3 
   

8. The remainder: The final result is the remainder (3).

Final Solution

Therefore, (x² + x - 17) ÷ (x - 4) = x + 5 + 3/(x - 4)