Question

Find the reamainder when following polynomial is divided by x+1
x³+ 3x² + 3x+ 1​

Answer 1

Remainder = 0

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GivEn:

• Dividend = x³ + 3x² + 3x + 1

• Divisor = x + 1

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To find:

• Remainder

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SoluTion:

Using Remainder theorem which is,

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If a polynomial p(x) is divided by the binomial (x - a), the remainder obtained is p(a).

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Here, Divisor = (x + 1)

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which is a factor of p(x) = 0

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$:\implies\sf x + 1 = 0$

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$:\implies\bf \red{x = -1}$

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★ Let $\sf p(x) = x^3 + 3x^2 + 3x + 1$

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$\;\;\;\;\;\;\;\;\small\sf \underline{Put\; x = -1}$

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$:\implies\sf p( -1) = (-1)^3 + 3(-1)^2 + 3(-1) + 1$

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$:\implies\sf p( -1) = - 1 + 3 - 3 + 1$

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$:\implies{\underline{\boxed{\sf{\purple{p(-1) = 0}}}}}\;\bigstar$

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$\therefore$ Hence, Remainder = p(-1) = 0.

Answer 2

By Using Remainder Theorem :

g(x) = x + 1 = 0

→ x = 0 - 1

.°. x = -1

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p(x) = x³+ 3x² + 3x + 1

→ p(-1) = (-1)³ + 3(-1)² + 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

.°. The remainder is 0...