How do you find the quotient of #(k^2-5k-24)div(k-8)#?

Question

Eva Abramson · Accepted Answer

Quotient is #(k+3)# #(k^2-5k-24)/(k-8) or (k^2-8k+3k-24)/(k-8) or (k(k-8)+3(k-8))/(k-8) or(cancel((k-8))(k+3))/cancel((k-8))= (k+3)# [Ans]

Jace Anderson · Answer

undefined To find the quotient of (k^2-5k-24) divided by (k-8), you can use long division or synthetic division.

Using long division:
- Divide the first term of the numerator (k^2) by the first term of the denominator (k). This gives you k.
- Multiply the entire denominator (k-8) by k, which gives you k^2-8k.
- Subtract this result from the numerator (k^2-5k-24) to get -3k-24.
- Bring down the next term (-3k) and repeat the process.
- Divide (-3k) by (k), which gives you -3.
- Multiply the entire denominator (k-8) by -3, which gives you -3k+24.
- Subtract this result from the previous result (-3k-24) to get 0.
- There is no remainder, so the quotient is k-3.

Using synthetic division:
- Write the coefficients of the numerator (1, -5, -24) in descending order.
- Write the root of the denominator (8) outside the division symbol.
- Bring down the first coefficient (1).
- Multiply the root (8) by the first coefficient (1), which gives you 8.
- Add this result (8) to the second coefficient (-5), which gives you 3.
- Multiply the root (8) by the new result (3), which gives you 24.
- Add this result (24) to the third coefficient (-24), which gives you 0.
- The resulting coefficients (1, 3, 0) represent the quotient. So, the quotient is k^2+3k+0, which simplifies to k^2+3k.