r^3-24r-5 / r-5

How to divide r^3-24r-5 / r-5 quickly with less steps ?

Thanks

well, you could guess

but it only took me a minute to do long division

r^2 + 5 r + 1

Thank you for your quick reply.

Can you please share the work ? Guess work in math could land up in wrong spot.

####### r^2 + 5 r + 1

#######_______________________
(r-5) | r^3 + 0 r^2 - 24 r - 5
####### r^3 - 5 r^2
#######_______________________
############# 5 r^2 - 24 r - 5
############# 5 r^2 - 25 r
############# ________________
#################### 1 r - 5
#################### 1 r - 5
#####################________
###################### R = 0

Thank you.

You are welcome.

To divide the expression (r^3 - 24r - 5) by (r - 5) quickly with fewer steps, you can use synthetic division. Here's how:

Step 1: Set up the synthetic division table:

5 | 1 -24 0 -5
|___________

Step 2: Bring down the first coefficient of the dividend (r^3 term):

5 | 1 -24 0 -5
|___________
1

Step 3: Multiply the divisor (5) by the result (1) and write it under the next term of the dividend (multiply both numbers in the row above by 5):

5 | 1 -24 0 -5
|___________
1
-------
5

Step 4: Add the result (5) to the next coefficient of the dividend (-24) and write the sum on the next row:

5 | 1 -24 0 -5
|___________
1
-------
5
-19

Step 5: Repeat steps 3 and 4 until you reach the last coefficient of the dividend:

5 | 1 -24 0 -5
|___________
1
-------
5
-19
95
______________
1 -19 95

Step 6: The final row of the synthetic division represents the coefficients of the quotient. In this case, the quotient is given by (1 - 19r + 95r^2).

Therefore, the division of (r^3 - 24r - 5) by (r - 5) gives a quotient of (1 - 19r + 95r^2).