Question

The remainders obtained when x³ + x² – 9x – 9 is divided by x, x + 1 and x + 2 respectively are _________.

Answer 1

Let f(x) = x³ + x² – 9x – 9

To find the remainder obtained when x³ + x² – 9x – 9 is divided by x,

we use remainder theorem, put x = 0.

f(0) is the remainder.

Now,

f(0) = (0)³ + (0)² – 9(0) – 9
= –9

Hence, the remainder obtained when x³ + x² – 9x – 9 is divided by x is –9.

To find the remainder obtained when x³ + x² – 9x – 9 is divided by x + 1,

put x +1 = 0.

f(–1) is the remainder.

Now,

f(–1) = (–1)³ + (–1)² – 9(–1) – 9
= –1 + 1 + 9 – 9
= 0

Hence, the remainder obtained when x³ + x² – 9x – 9 is divided by x + 1 is 0.

To find the remainder obtained when x³ + x² – 9x – 9 is divided by x + 2,

put x +2 = 0.

f(–2) is the remainder.

Now,

f(–2) = (–2)³ + (–2)² – 9(–2) – 9
= –8 + 4 + 18 – 9
= 5

Hence, the remainder obtained when x³ + x² – 9x – 9 is divided by x + 2 is 5.


Hence, the remainders obtained when x³ + x² – 9x – 9 is divided by x, x + 1 and x + 2 respectively are –9, 0 and 5.