Question

Use the remainder theorem to determine the remainder when d4 + 2d2 + 5d − 10 is divided by d + 4. A. 42 B. 258 C. 126 D. 106

Answer 1

The answer would be B . 258

Answer 2

Answer: The correct option is (B) 258.

Step-by-step explanation: We are give to use the remainder theorem to determine the remainder when

`d^4+2d^2+5d-10` is divided by
`d+4.`

Remainder Theorem : If p(x) is a polynomial in x and a is any real number, then the remainder when p(x) is divided by (x - a) is p(a).

For the given division, we have

`p(d)=d^4+2d^2+5d-10\\\\d-a=d+4~~~~~\Rightarrow a=-4.`

Therefore, the remainder when p(d) is divided by (d + 4) is given by

`p(-4)\\\\=(-4)^4+2* (-4)^2+5*(-4)-10\\\\=256+32-20-10\\\\=288-30\\\\=258.`

Thus, the required remainder is 258.

Option (B) is CORRECT.