Question

x³+3x²+3x+1 by g (x) =x+1​

Answer 1

We are asked to find the reminder when p(x) is divided by g(x)!

Given that:

• p(x) = x³ + 3x² + 3x + 1

• g(x) = x + 1

Solution:

• Remainder = 0

Required solution:

† Firstly let us find out the value of x by putting g(x) as 0!

⇒ g(x) = x + 1 [Given]

⇒ g(0) = x + 1

⇒ 0 = x + 1

⇒ 0 - 1 = x

⇒ -1 = x

• ∴ x = -1

† Now let us put x as -1 in p(x)!

⇒ p(x) = x³ + 3x² + 3x + 1

⇒ p(x) = (-1)³ + 3(-1)² + 3(-1) + 1

⇒ p(x) = -1 + 3(1) + (-3) + 1

⇒ p(x) = -1 + 3 - 3 + 1

⇒ p(x) = -1 + 1 + 3 -3

⇒ p(x) = 0 + 3 - 3

⇒ p(x) = 0 + 0

⇒ p(x) = 0

• ∴ Reminder = 0 $\:$