Question

What number should be added to 3$x^3$ + 2$x^2$ - 7x so that when the resulting polynomial is divided by x - 2, the remainder is 2?

• A. 4
• B. - 2
• C. - 4
• D. 5

Answer 1

The correct option is C

- 4

Let the number added be a so the resulting polynomial is 3$x^3$ + 2$x^2$ - 7x + a

Given, when this polynomial is divided by x + 1, the remainder is 2

$\to$ 3$(-1{)}^3$​ + 2$(-1{)}^2$​ - 7(-1) + a = 2

$\to$ - 3 + 2 + 7 + a = 2

$\to$ 6 + a = 2

$\to$ a = - 4