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Suppose $p(x)$ is a function such that $p(x) + (x^5+3x^3+9x) = (7x^3+24x^2+25x+1)$. Express $p(x)$ as a polynomial with the degrees of the terms in decreasing order.

 Dec 4, 2014

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 #1
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$$\\p(x) = (7x^3+24x^2+25x+1)\quad -\quad (x^5+3x^3+9x)\\
p(x) = 7x^3+24x^2+25x+1\quad -x^5-3x^3-9x\\
p(x) = -x^5+7x^3-3x^3+24x^2+25x-9x+1\quad \\
p(x) = -x^5+4x^3+24x^2+16x+1\quad \\$$

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 Dec 4, 2014

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 #1
avatar+118608 
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Best Answer

$$\\p(x) = (7x^3+24x^2+25x+1)\quad -\quad (x^5+3x^3+9x)\\
p(x) = 7x^3+24x^2+25x+1\quad -x^5-3x^3-9x\\
p(x) = -x^5+7x^3-3x^3+24x^2+25x-9x+1\quad \\
p(x) = -x^5+4x^3+24x^2+16x+1\quad \\$$

Melody Dec 4, 2014

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