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

- 61 x + 65

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2 x - 15

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- 15 x + 2

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None of these

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Solution

The correct option is B None of these
$x^{2} + 2 x - 3) ¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ 4 x^{4} + 2 x^{3} + 2 x^{2} + x - 1$ ( $4 x^{2} - 6 x + 26$
$4 - x^{4} + - 8 x^{3} - + 12 x^{2} - ---------------- -$
$- 6 x^{3} + 14 x^{2} + x - 1$
$- + 6 x^{3} - + 12 x^{2} + - 18 x - ------------------ -$
$26 x^{2} - 17 x - 1$
$+ - 26 x^{2} + - 52 x - + 78 - ----------------- -$
$- 69 x + 77$
We have to add $69 x - 77$ so that $4 x^{4} + 2 x^{3} + 2 x^{2} + x - 1$ is completely divisible by $x^{2} + 2 x - 3$ .

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What must be added to f(x)=4x4+2x3+2x2+x−1 so that the resulting polynomial is divisible by g(x)=x2+2x−3

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