Question

What is the remainder when (2x3 + 4x2 − 32x − 40) ÷ (x − 4)?

Answer 1

The remainder when dividing is the same as the value when evaluating with x = 4. This is called the remainder theorem.
2(4)^3 + 4(4)^2 - 32(4) - 40
2(64) + 4(16) - 32(4) - 40
128 + 64 - 128 - 40
24

Answer 2

Remainder = 24

Explanation:

Given:
`(2x^3+4x^2-32x-40)/ (x-4)`

Here we are given a division of rational number. Using synthetic division to find remainder.

Step 1: Multiply 4 with 2 and write below 4 and add them to get 12

Step 2: Multiply 12 with 4 and write below -32 and add them to get 16

Step 3: Multiply 16 with 4 and write below -40 and add them to get 24

24 is remainder.

4 | 2 4 -32 -40 |

8 48 64

2 12 16 24

At last we get number is 24.

Please see the attachment for synthetic division.

Hence, The remainder of division is 24