Find the remainder when 27 x 3-9 x 2-5 x -1 is divided by 3 x -1A- x-y B- x2-yC- x2-yD- x-y

The correct option is C x2 – y Let p(x)=27x^3 9x^2 +5x 1 3x+1 = 0 ⇒ x = 1/3 Put x= 1/3 in the given expression p( 1/3) = 27 × ( 1/3)^3 9 × ( 1/3)^2 + 5× ...

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Standard X

Mathematics

Algebraic Expressions

Find the rema...

Question

Find the remainder when $27 x^{3} - 9 x^{2} + 5 x - 1$ is divided by $3 x + 1$

x + y

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x – y

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x² + y

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x² – y

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Solution

The correct option is D
x² – y

Let $p (x) = 27 x^{3} - 9 x^{2} + 5 x - 1$

$3 x + 1 = 0$

$\Rightarrow$ $x = \frac{- 1}{3}$
Put $x = - \frac{1}{3}$ in the given expression
$p (\frac{- 1}{3}) = 27 \times (\frac{- 1}{3})^{3} - 9 \times (\frac{- 1}{3})^{2} + 5 \times \frac{- 1}{3} - 1$

$\Rightarrow$ $27 \times \frac{- 1}{27} - 9 \times \frac{1}{9} + 5 \times \frac{- 1}{3} - 1$

$\Rightarrow$ $- 1 - 1 - \frac{5}{3} - 1$

$\Rightarrow$ $- \frac{14}{3}$

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Find the remainder when 27x3−9x2+5x−1 is divided by 3x+1

The correct option is D x2 – y Let p(x)=27x3−9x2+5x−1 3x+1=0 ⇒ x=−13 Put x=−13 in the given expression p(−13) = 27×(−13)3−9×(−13)2+5×−13−1 ⇒ 27×−127−9×19+5×−13−1 ⇒ −1−1−53−1 ⇒ −143

Find the remainder when $27 x^{3} - 9 x^{2} + 5 x - 1$ is divided by $3 x + 1$