The expression that should be added to the polynomial fx-x4-2 x3-2 x2-x-1- so that it should be exactly divisible by x2-2 x-3 is

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Standard X

Mathematics

Division Algorithm for a Polynomial

The expressio...

Question

The expression that should be added to the polynomial f(x) = x⁴ + 2x³ – 2x² + x + 1, so that it should be exactly divisible by (x² + 2x – 3) is

2 - x

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x³ - 3

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x + 2

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x - 4

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Solution

The correct option is D
x - 4

Divide f(x) by g(x) and find the remainder r(x) = –x + 4. Then minus of r(x) = x – 4 should be added.

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Similar questions

Q. What must be added to the polynomial

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

so that the resulting polynomial is exactly divisible by

x^{2} + 2 x - 3

The expression that should be subtracted from the polynomial f(x) = x⁴ + 2x³ -13x² - 12x + 21 so that the resulting polynomial is exactly divisible by g(x) = x² – 4x + 3 is

Q. What should be added to

(x^{4} - 1)

so that it is exactly divisible by

(x^{2} + 2 x + 1)

Q. What must be added to

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

so that the resulting polynomial is divisible by

g (x) = x^{2} + 2 x - 3

Q. What must be added to

x^{4} + 2 x^{3} - 2 x^{2} + x - 1

. So that result is exactly divisible by

x^{2} + x - 2

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The expression that should be added to the polynomial f(x) = x4 + 2x3 – 2x2 + x + 1, so that it should be exactly divisible by (x2 + 2x – 3) is

The correct option is D x - 4Divide f(x) by g(x) and find the remainder r(x) = –x + 4. Then minus of r(x) = x – 4 should be added.

The expression that should be added to the polynomial f(x) = x⁴ + 2x³ – 2x² + x + 1, so that it should be exactly divisible by (x² + 2x – 3) is

The correct option is D
x - 4

Divide f(x) by g(x) and find the remainder r(x) = –x + 4. Then minus of r(x) = x – 4 should be added.