-divided-by-(a-5).jpeg "(a^2-28) Divided By (a-5)")
Dividing (a^2 - 28) by (a - 5)
This problem involves dividing a polynomial by a binomial. We can use long division to solve it. Here's how:
Step 1: Set up the Long Division
a + 5
a - 5 | a^2 + 0a - 28
- We write the dividend (a^2 - 28) inside the division symbol. Notice that we've added a 0a term as a placeholder for the missing linear term.
- The divisor (a - 5) is written outside the division symbol.
Step 2: Divide the Leading Terms
- Divide the leading term of the dividend (a^2) by the leading term of the divisor (a). This gives us a.
- Write a above the division symbol, aligned with the a^2 term.
a + 5
a - 5 | a^2 + 0a - 28
a^2 - 5a
Step 3: Multiply and Subtract
- Multiply the divisor (a - 5) by the term we just wrote above (a). This gives us a^2 - 5a.
- Write this result below the dividend.
- Subtract the two polynomials:
a + 5
a - 5 | a^2 + 0a - 28
a^2 - 5a
-------
5a - 28
Step 4: Bring Down the Next Term
- Bring down the next term from the dividend (-28).
a + 5
a - 5 | a^2 + 0a - 28
a^2 - 5a
-------
5a - 28
Step 5: Repeat Steps 2-4
- Divide the leading term of the new polynomial (5a) by the leading term of the divisor (a). This gives us 5.
- Write 5 above the division symbol, aligned with the constant term.
- Multiply the divisor (a - 5) by 5. This gives us 5a - 25.
- Subtract the two polynomials:
a + 5
a - 5 | a^2 + 0a - 28
a^2 - 5a
-------
5a - 28
5a - 25
-------
-3
Step 6: Remainder
- We're left with a remainder of -3.
The Result
Therefore, (a^2 - 28) divided by (a - 5) is a + 5 with a remainder of -3. We can express this as:
(a^2 - 28) / (a - 5) = a + 5 - 3/(a - 5)