How to find the quotient and remainder

Question

use synthetic division to find the quotient and remainder

Answer 1

1] Rewrite the equation so that we have variables of x with all exponents:

-4x³ - x² + 0x - 12 ÷ (x + 4)

2] Next, set the component you are dividing by equal to zero and solve for x:

(x+4) = 0 and so after solving we have: x = -4

3] Now we need to perform synthethic division:

First write out -4 (from Step 2 above) and the numbers in front of the variables as well as the constant -12:

-4 || -4 -1 0 -12

We next bring down the second -4 and multiply the -4 from Step 2 by it to get 16. Once we have that we place it under the next number which is -1.

-4 || -4 -1 0 -12

-4

-4 || -4 -1 0 -12

16

-4

Now add the -1 and 16 to get 15 and place underneath.

-4 || -4 -1 0 -12

16

-4 15

Now multiply -4 by 15 to get -60 and place under the next number which is zero and then add 0 and -60. This is the general process we will repeat until the last number.

-4 || -4 -1 0 -12

16 -60

-4 15

Then once we repeat the above process two more times we get:

-4 || -4 -1 0 -12

16 -60 240

-4 15 -60 228

4] The last number on the bottom far right corner is our remainder (228).

5] Now we take our original equation from above ( -4x³ - x² + 0x - 12 ) and replace the numerical values with our new ones that we acquired ( -4, 15, -60 and 228) to get:

-4x³ + 15x² - 60 + 228

6) Next, since we are diving the whole thing by (x+4) we divide by x for each variable in the equation to get:

-4x² + 15x - 60 + 228

Since our remainder (228) is not zero we divide it by (x+4) and leave it in that format.

-4x² + 15x - 60 + (228 / (x+4))

This is our quotient and our remainder is 228.

I hope you found this helpful!