Jasonbradley
Home

(a2-28)÷(a-5)

3 min read Jun 16, 2024
(a2-28)÷(a-5)

Simplifying the Expression (a² - 28) ÷ (a - 5)

This article will guide you through simplifying the expression (a² - 28) ÷ (a - 5).

Understanding the Expression

The expression involves:

  • Division: We are dividing the polynomial (a² - 28) by the binomial (a - 5).

Simplifying using Polynomial Long Division

One way to simplify this expression is using polynomial long division. Here's how it works:

  1. Set up the division:

        ________
a - 5 | a² - 28

  2. Divide the leading terms:

    • The leading term of the divisor (a - 5) is 'a'.
    • The leading term of the dividend (a² - 28) is 'a²'.
    • a² ÷ a = a. Write 'a' above the line.
        a      
a - 5 | a² - 28

  3. Multiply the quotient by the divisor:

    • a * (a - 5) = a² - 5a. Write this below the dividend.
        a      
a - 5 | a² - 28 
        a² - 5a

  4. Subtract:

    • (a² - 28) - (a² - 5a) = 5a - 28. Bring down the -28.
        a      
a - 5 | a² - 28 
        a² - 5a 
        -------
             5a - 28

  5. Repeat steps 2-4:

    • The leading term of the new dividend is '5a'.
    • 5a ÷ a = 5. Write '+ 5' next to the 'a' above the line.
        a + 5  
a - 5 | a² - 28 
        a² - 5a 
        -------
             5a - 28
             5a - 25

  6. Subtract:

    • (5a - 28) - (5a - 25) = -3. This is our remainder.
        a + 5  
a - 5 | a² - 28 
        a² - 5a 
        -------
             5a - 28
             5a - 25 
             -------
                 -3

Therefore, (a² - 28) ÷ (a - 5) = a + 5 - 3/(a - 5)

Conclusion

The simplified form of (a² - 28) ÷ (a - 5) is a + 5 - 3/(a - 5). This result can be useful for further algebraic manipulations and problem-solving.

Related Post

Featured Posts