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.
+9466 p(x) + (x5 + 3x3 + 9x) = (7x3 + 24x2 + 25x + 1)
Subtract (x5 + 3x3 + 9x) from both sides of the equation.
p(x) = (7x3 + 24x2 + 25x + 1) - (x5 + 3x3 + 9x)
p(x) = 7x3 + 24x2 + 25x + 1 - x5 - 3x3 - 9x
p(x) = -x5 + 7x3 - 3x3 + 24x2 + 25x - 9x + 1
p(x) = -x5 + 4x3 + 24x2 + 16x + 1
+9466 p(x) + (x5 + 3x3 + 9x) = (7x3 + 24x2 + 25x + 1)
Subtract (x5 + 3x3 + 9x) from both sides of the equation.
p(x) = (7x3 + 24x2 + 25x + 1) - (x5 + 3x3 + 9x)
p(x) = 7x3 + 24x2 + 25x + 1 - x5 - 3x3 - 9x
p(x) = -x5 + 7x3 - 3x3 + 24x2 + 25x - 9x + 1
p(x) = -x5 + 4x3 + 24x2 + 16x + 1
