Question

if x cube + 3 X square + 3 X + 1 is divided by X + 1 then the remainder is​

Answer 1

SOLUTION.

Given –

→ p(x) = x³ + 3x² + 3x + 1

→ x + 1 = 0

→ x = -1

So, when p(x) is divided by x + 1,

→ Remainder = p(-1)

Therefore,

→ p(-1) = (-1)³ + 3 × (-1)² + 3 × (-1) + 1

→ p(-1) = -1 + 3 - 3 + 1

→ p(-1) = 0

✠ Therefore, when p(x) is divided by x + 1, remainder is 0 i.e., x + 1 is a factor of p(x).

ANSWER.

• Remainder = 0.

CONCEPT.

• Remainder Theorem: If f(x) is a polynomial divided by (x + a) where a is real number, then remainder = f(-a).

Answer 2

Given :-

x³ + 3x² + 3x + 1 is divided by x + 1

To Find :-

Remainder

Solution :-

Remainder theorem

x + 1 = 0

x = 0 - 1

x = -1

Now

p(x) = x³ + 3x² + 3x + 1

Put the value of x

p(-1) = (-1)³ + 3(-1)² + 3(-1) + 1

p(-1) = (-1 × -1 × -1) + 3(-1 × -1) + 3(-1) + 1

p(-1) = -1 + 3(1) + (-3) + 1

p(-1) = -1 + 3 - 3 + 1

p(-1) = (-1 + 1) + (3 - 3)

p(-1) = 0 + 0

p(-1) = 0

Thus

Remainder is 0