How much is $y^{4} - 12 y^{2} + y + 14$ greater than $17 y^{3} + 34 y^{2} - 51 y + 68$ .

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Solution

Let the given polynomial is greater than the other by $M$
According to question,
$17 y^{3} + 34 y^{2} - 51 y + 68 + M = y^{4} - 12 y^{2} + y + 14$
$\Rightarrow M = (y^{4} - 12 y^{2} + y + 14) - (17 y^{3} + 34 y^{2} - 51 y + 68)$
$\Rightarrow M = y^{4} - 12 y^{2} + y + 14 - 17 y^{3} - 34 y^{2} + 51 y - 68$
Collecting like terms,
$\Rightarrow M = y^{4} - 17 y^{3} - 12 y^{2} - 34 y^{2} + y + 51 y + 14 - 68$
$\Rightarrow M = y^{4} - 17 y^{3} - 46 y^{2} + 52 y - 54$

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