Question

What number must be added to 2x³ + x² + 17x + 10 so that the resulting polynomial is exactly divisible by (x + 2)?

Answer 1

Let the number added be k

f(x) = 2x³ + x² + 17x + 10 + k

Let x + 2 = 0

x = −2

f(−2) = 2(−2)³ + (−2)² + 17(−2) + 10 + k

= −16 + 4 − 34 + 10 + k

= −36 + k

Set the remainder f(−2) equal to zero to find the value of k

f(−2) = 0

−36 + k = 0

k = 36

∴ The number that must be added to the polynomial so that the resulting polynomial is exactly divisible by (x + 2) is 36.