(k^2-7k+10) Divide By (k-1)

Jasonbradley

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Jun 16, 2024

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Dividing (k^2 - 7k + 10) by (k - 1)

In this article, we will explore how to divide the polynomial (k^2 - 7k + 10) by the binomial (k - 1). We can achieve this using polynomial long division.

Polynomial Long Division

1. Set up the division: Write the dividend (k^2 - 7k + 10) inside the division symbol and the divisor (k - 1) outside.

       _________
   k-1 | k^2 - 7k + 10 
   

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

       k     
   k-1 | k^2 - 7k + 10 
   

3. Multiply and subtract: Multiply the quotient (k) by the divisor (k - 1) and write the result below the dividend.

       k     
   k-1 | k^2 - 7k + 10 
        k^2 - k
   

   Subtract the result from the dividend.

       k     
   k-1 | k^2 - 7k + 10 
        k^2 - k
       --------
          -6k + 10
   

4. Bring down the next term: Bring down the next term from the dividend (+10).

       k     
   k-1 | k^2 - 7k + 10 
        k^2 - k
       --------
          -6k + 10 
   

5. Repeat steps 2-4: Divide the leading term of the new dividend (-6k) by the leading term of the divisor (k). This gives us -6. Write this quotient next to the previous quotient.

       k - 6   
   k-1 | k^2 - 7k + 10 
        k^2 - k
       --------
          -6k + 10 
   

   Multiply -6 by (k - 1) and write the result below.

       k - 6   
   k-1 | k^2 - 7k + 10 
        k^2 - k
       --------
          -6k + 10 
          -6k + 6
   

   Subtract the result.

       k - 6   
   k-1 | k^2 - 7k + 10 
        k^2 - k
       --------
          -6k + 10 
          -6k + 6
       --------
                4
   

6. The remainder: The final result is 4, which is our remainder.

Result

Therefore, (k^2 - 7k + 10) divided by (k - 1) is k - 6 with a remainder of 4. This can also be written as:

(k^2 - 7k + 10) / (k - 1) = k - 6 + 4/(k - 1)