For a polynomial px-2 x4-3 x3-2 x2-2 x-1 what is the remainder when it-s divided by x-4 -

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Remainder Theorem

For a polynom...

Question

For a polynomial p(x) =2x⁴ – 3x³ + 2x² + 2x - 1 what is the remainder when it’s divided by x+4?

p(4)

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p(-2)

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p(2)

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p(-4)

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Solution

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p(x)= 2x⁴ - 3x³ + 2x² + 2x - 1 is divided by (x - 2) and q(x) = 3x³ - 2x² + x - 1 is divided by (x - 1). So, twice the sum of the remainders is:

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

2 x - 1

(7 x^{2} + x + 5)

(3 x^{3} - 2 x^{2} + 7 x - 5) \div (x + 3)

The remainder when $3 x^{3} + 2 x^{2} - x + 4$ is divided by $3 + 2 x$ is $\frac{- 1}{8}$ .

3 x^{3} + 2 x^{2} - x + 4

3 + 2 x

\frac{- 1}{8}

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