Question

What must be added to x³ + 7x² + 3x + 2 so that the result is completely divisible by (x + 2)?

Options

• −40

• −16

• 16

• 40

Answer 1

−16

Explanation:

Using the remainder theorem,

If polynomial P(x) is divided by (x − a), the remainder is P(a).

Given: x + 2 = 0

x = −2

Substituting x = −2 into the polynomial x³ + 7x² + 3x + 2, we get:

⇒ P(−2) = (−2)³ + 7(−2)² + 3(−2) + 2

= −8 + 28 − 6 + 2

= 20 − 6 + 2

= 16

For a polynomial to be completely divisible by x + 2, the remainder must be 0.

We have a remainder of 16, we need to add a number k such that the new remainder becomes zero, i.e.,:

k + 16 = 0

k = −16