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Remainder Theorem

The remainder...

Question

The remainder obtained when the polynomial $x^{4} - 3 x^{2} - 2 x - 3$ is divided by x-2 is

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-4

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-3

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Solution

The correct option is D -3
$f (x) = x^{4} - 3 x^{2} - 2 x - 3$ the remainder
when $f (x)$ is divided by $x - 2$ is
$f (2)$ from remainder theoren
So,
$f (2) = 2^{4} - 3 \times 2^{2} - 2 \times 2 - 3$
$= 16 - 12 - 4 - 3$
$= - 3$
$f (2) = - 3$
So, remainder $= - 3$

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The polynomial x⁴- 2x³+ 3x²- ax + b when divided by x +1 and x -1 give remainder 19 and 5 respectively . Find the remainder when the polynomial is divided by x -3

Q. Assertion (A) : The remainder obtained when the polynomial

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Q. A polynomial

f (x)

leaves remainder

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when divided by

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and

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when divided by

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when divided by

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The remainder obtained when the polynomial x4−3x2−2x−3 is divided by x-2 is

The correct option is D -3f(x)=x4−3x2−2x−3 the remainderwhen f(x) is divided by x−2 isf(2) from remainder theorenSo,f(2)=24−3×22−2×2−3=16−12−4−3=−3f(2)=−3So, remainder =−3

The remainder obtained when the polynomial $x^{4} - 3 x^{2} - 2 x - 3$ is divided by x-2 is

The correct option is D -3
$f (x) = x^{4} - 3 x^{2} - 2 x - 3$ the remainder
when $f (x)$ is divided by $x - 2$ is
$f (2)$ from remainder theoren
So,
$f (2) = 2^{4} - 3 \times 2^{2} - 2 \times 2 - 3$
$= 16 - 12 - 4 - 3$
$= - 3$
$f (2) = - 3$
So, remainder $= - 3$