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:

Set up the division:
________ a  5  a²  28

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

Multiply the quotient by the divisor:
 a * (a  5) = a²  5a. Write this below the dividend.
a a  5  a²  28 a²  5a

Subtract:
 (a²  28)  (a²  5a) = 5a  28. Bring down the 28.
a a  5  a²  28 a²  5a  5a  28

Repeat steps 24:
 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

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 problemsolving.