Question

Find the remainder when x^3+3x^2+3x+1 is divided by x+1

Answer 1

Step-by-step explanation:

Hi Dear !!

F(x) = X³ + 3X² + 3X + 1

Here, ( X+1) is a factor of F(x) .

Then, X + 1 = 0 I.e X = -1

Put the value of x in F(x) .

F(-1) = (-1)³ + 3 * (-1)² + 3 * (-1) + 1

=> -1 + 3 - 3 + 1 = 0

Hence,

Remainder = 0 ..

Hope it will help you :))

Answer 2

Answer:

Hey mate, Good evening ❤

#Here's ur answer...☆☆☆

Step-by-step explanation:

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The remainder theorem states that when a polynomial, f(x), is divided by a linear polynomial , x - a, the remainder of that division will be equivalent to f(a). In other words, if you want to evaluate the function f(x) for a given number, a, you can divide that function by x - a and your remainder will be equal to f(a).

$\bold{given \: \: p(x) = {x}^{3} + 3 {x}^{2} + 3x + 1 } \\ \bold{g(x) = x + 1}\\ \bold{p(x) = g(x) \times q(x) + r(x)} \\ \bold{ \green{= > p(x)will \: be = r(x) \: when \: g(x) = 0}}$

$= > g(x) = 0 \\ = > x + 1 = 0 \\ = > x = - 1 \\ \green{ \bold{then \: p(1) = remainder}} \\ p(1) = - 1 {}^{3} + 3 ({-1})^{2} + 3(-1) + 1 \\ = > p(1) = 0 \\ \red{ \bold{hence \: remainder = 8}}$

▶️Hope this helps you ✌✌

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