Question

By remainder theorem find the remainder when p (x)= x^3-2x^2-4x-1 g (x)=x+1

Answer 1

Answer:

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Step by step solution:

$Given \ p(x)=x^{3}-2 x^{2}-4x-1 \ and \ g(x)= x+1\\\\we \ have \ to \ find \ remainder.\\\\putting \ g(x) \ value \ -1 \ in \ p(x)\\\\p(-1)=(-1)^{3}-2(-1^{2})-4(-1)-1\\\\p(-1)=-1-2+4-1\\\\p(-1)=4-4=0\\\\So \ remainder \ is \ 0$

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Answer 2

Solution :-

As given :-

p(x) = x³ - 2x² - 4x - 1

g(x) = x + 1

Then zero of g(x)

x + 1 = 0

→ x = -1

Now by putting the value of x = -1 in f(x)

p(-1) = (-1)³ - 2(-1)² - 4(-1) - 1

p(-1) = -1 -2 + 4 - 1

p(-1) = -4 + 4

p(-1) = 0

Therefore (-1) is a factor of p(x)

Hence x + 1 is a factor of p(x)

Hence g(x) is a factor of p(x)