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Remainder Theorem

fx=4 x3-12 x2...

Question

f(x) = 4x³ − 12x² + 14x − 3, g(x) 2x − 1

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Solution

Let us denote the given polynomials as

We have to find the remainder whenis divided by.

By the remainder theorem, whenis divided bythe remainder is

Now we will calculate the remainder by actual division

So the remainder by actual division is

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Similar questions

Q. Find the remainder when the polynomial f(x) = 4x³ − 12x² + 14x − 3 is divided by (2x − 1).

Q. By Remainder Theorem find the remainder, when

p (x)

g (x)

p (x) = 4 x^{3} - 12 x^{2} + 14 x - 3, g (x) = 2 x - 1

Q. In the following case, use the remainder theorem and find the remainder when

p (x)

g (x)

p (x) = 4 x^{3} - 12 x^{2} + 14 x - 3 g (x) = 2 x - 1

Divide $4 x^{3} + 12 x^{2} + 11 x + 3 b y x + 1$ and then find the quotient.

Q. Determine the intervals in which

f

is inreasing and decreasing

f : R \to R, f (x) = 3 x^{4} - 4 x^{3} - 12 x^{2} + 5

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