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Question

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


Solution

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


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