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).