Find the remainder when px-3 x2-x-1 is divided by gx-1-xA- 2B- 3C- -1D- -1

The correct option is D +1 Method 1: enclose [ 3x 2; x +1 longdiv3x^2+x 1; 3x^2+3x2; 2x 1; 2x 2; ...

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Standard X

Mathematics

Division Algorithm for a Polynomial

Find the rema...

Question

Find the remainder when p(x) = $3 x^{2} + x + - 1$ is divided by g(x) = 1 + x.

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-1

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Solution

The correct option is D
+1

Method 1:

$\begin{matrix} 3 x - 2 x + 1 3 x^{2} + x - 1 3 x^{2} + 3 x - -------- - - 2 x - 1 - 2 x - 2 - ------- - 1 \end{matrix}$

Method 2:
Here $p (x) = 3 x^{2} + x - 1$
The zero of $g (x) = x + 1$ is $- 1$
$p (- 1) = 3 x (- 1)^{2} + (- 1) - 1 = 3 - 1 - 1 = 1$
So by the remainder theorem, 1 is the remainder.

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Find the remainder when p(x) = 3x2+x+−1 is divided by g(x) = 1 + x.

The correct option is D +1 Method 1: 3x−2x+13x2+x−1 3x2+3x––––––––––2 −2x−1 −2x−2––––––––– 1 Method 2: Here p(x)=3x2+x−1 The zero of g(x)=x+1 is −1 p(−1)=3x(−1)2+(−1)−1=3−1−1=1 So by the remainder theorem, 1 is the remainder.

Find the remainder when p(x) = $3 x^{2} + x + - 1$ is divided by g(x) = 1 + x.